55 + Interview Questions in PARTIAL-FRACTIONS IN GENERAL AWARENESS

1.	Resolve `(3x+5)/((x+2)(3x-1))` into partial fractions.
Answer» In the given fraction, the denominator has two linear,non-repeated factors. `:.` The given fraction can be written as the sum of two partial fractions. Let `(3x+5)/((x+2)(3x-1))=(A)/(x+2)+(B)/(3x-1)` `implies3x+5=A(3x-1)+B(x+2)` .......`(1)` Put `x=-2` in Eq. `(1)`, `implies3(-2)+5=A[3(-2)-1]+B(-2+2)-1=-7AimpliesA=(1)/(7)` Comparing the costant the constant terms on both sides of Eq. `(1)`, we have `5=-A+2B` `5=-(1)/(7)+2B` or `B=(18)/(7)` `:. (3x+5)/((x+2)(3x-1))=((1)/(7))/(x+2)+((18)/(7))/(3x-1)=(1)/(7)[(1)/(x+2)+(18)/(3x-1)]`

Discussion

2.	Resolve `(ax-b)/((x+1)^(2))` into partical fractions.A. `(a)/(x+1)+(a+b)/((x+1)^(2))`B. `(a)/(x+1)+(a-b)/((x+1)^(2))`C. `(a)/(x+1)-(a-b)/((x+1)^(2))`D. `(a)/(x+1)-(a+b)/((x+1)^(2))`
Answer» `(ax-b)/((x+1)^(2))=(A)/(x+1)+(B)/((x+1)^(2))`.

Discussion

3.	Resolve `(ax+b^(2))/(x^(2)-(a+b)^(2))` into partical fractions.A. `(a^(2)+ab+b^(2))/(2(a+b)(x-(a+b)))+(a^(2)+ab-b^(2))/(2(a+b)(x+(a+b)))`B. `(a^(2)+b^(2))/(2(a+b)(x-(a+b)))+(a^(2)-b^(2))/(2(a+b)(x+(a+b)))`C. `(a^(2)-b^(2))/(2(a+b)(x-(a-b)))+(a^(2)+b^(2))/(2(a+b)(x+(a+b)))`D. `(a^(2)+ab+b^(2))/(2(a+b)(x-(a+b)))-(a^(2)+ab-b^(2))/(2(a+b)(x+(a+b)))`
Answer» `(ax+b^(2))/(x^(2)-(a+b)^(2))=(A)/(x-(a+b))+(B)/(x+(a+b))`.

Discussion

4.	Resolve `(3x^(2)+7)/(x^(4)-3x^(2)+2)` into partical fractions.A. `(10)/(x^(2)-2)+(5)/(x-1)-(5)/(x+1)`B. `(13)/(x^(2)-2)+(5)/(x+1)-(5)/(x-1)`C. `(5)/(x^(2)-2)+(10)/(x-1)-(10)/(x+1)`D. `(5)/(x-1)-(5)/(x+1)-(13)/(x^(2)-2)`
Answer» Let `x^(2)=p`, then `(3x^(2)+7)/(x^(4)-3x^(2)+2)=(3p+7)/(p^(2)-3p+2)` Let `(3p+7)/(p^(2)-3p+2)=(A)/(p-1)+(B)/(p-2)` `implies(3p-7)/((p-1)(p-2))=(A(p-2)+B(p-1))/((p-1)(p-2))` Consider, `3p+7=A(p-2)+B(p-1)` Put `p=1`, `-A=10impliesA=-10` `p=2`, `B=13` `(3p+7)/(p^(2)-3p+2)=(13)/(p-2)-(10)/(p-1)` But `p=x^(2)` , `:. (3x^(2)+7)/(x^(4)-3p^(2)+2)=(13)/(x^(2)-2)-(10)/(x^(2)-1)` `=(13)/(x^(2)-2)-5[(1)/(x-1)-(1)/(x+1)]` `=(13)/(x^(2)-2)+(5)/(x+1)-(5)/(x-1)`.

Discussion

5.	If `(x^(3))/((x-1)(x-2))=Ax+B+(C )/(x-1)+(D)/(x-2)`, then `A,B,C` and `D`, respectively are ____________.A. `1,3,1,8`B. `1,-1,3,8`C. `1,3,-1,8`D. `-1,-3,1,8`
Answer» `(i)` Simplify L.H.S and R.H.S by taking L.C.M. `(ii)` Compare the like terms and obtain the required values.

Discussion

6.	Resolve `(1)/((x-4)(x^(2)+3))` into partical fractions.A. `(1)/(19)[(1)/(x-4)+(x+4)/(x^(2)+3)]`B. `(1)/(19)[(1)/(x-4)+(x+3)/(x^(2)+3)]`C. `(1)/(19)[(1)/(x-4)+(x+3)/(x^(2)+3)]`D. `(1)/(19)[(1)/(x-4)-(x+4)/(x^(2)+3)]`
Answer» `(1)/((x-4)(x^(2)+3))=(A)/(x-4)+(B)/(x^(2)+3)` `(1)/((x-4)(x^(2)+3))` `=(A(x^(2)+3)+(x-4)(Bx+C))/((x-4)(x^(2)+3))` Consider, `Ax^(2)+3A+bx^(2)+cx-4Bx-4C=1` `(A+B)x^(2)+(C-4B)x+3A-4C=1` Comparing the like terms, we get `A+B=0`, `C-4B=0` and `(3A-4C)=1` Solving the above equations, we get `A=(1)/(19)`, `B=(-1)/(19)`, `C=(-4)/(19)`. `:.(1)/((x-4)(x^(2)+3))=(1)/(19)[(1)/(x-4)-(x+4)/(x^(2)+3)]`

Discussion

7.	Resolve `(6x^(2)-14x+6)/(x(x-1)(x-2))` into partical fractions.A. `(2)/(x)+(3)/(x-1)+(1)/(x-2)`B. `(3)/(x)+(2)/(x-1)+(1)/(x-2)`C. `(1)/(x)+(2)/(x-1)+(3)/(x-2)`D. `(1)/(x)+(3)/(x-1)+(2)/(x-2)`
Answer» Let `(6x^(2)-14x+6)/(x(x-1)(x-2))=(A)/(x)+(B)/(x-1)+(C )/(x-2)` `(6x^(2)-14x+6)/(x(x-1)(x-2))` `=(A(x-1)(x-2)+Bx(x-2)+Cx(x-1))/(x(x-1)(x-2))` `6x^(2)-14x+6` `=A(x-1)(x-2)+Bx(x-2)+C(x-1)x` Put `x=1`, `6-14+6=B1(1-2)implies-2=-B` `impliesB=2`. Put `x=2`, `6(2)^(2)-14(2)+6=C(2-1)(2)` `2=2C` `1=C` Put `x=0`, `6=A(-1)(-2)impliesA=3` `:.(6x^(2)-14x+6)/(x(x-1)(x-2))=(3)/(x)+(2)/(x-1)+(1)/(x+2)`.

Discussion

8.	Resolve `(2x^(2)+8x+13)/((x+1)^(4))` into partical fractions.A. `(2)/((x+1)^(2))+(5)/((x+1)^(3))+(7)/((x+1)^(4))`B. `(1)/((x+1)^(2))+(5)/((x+1)^(3))+(7)/((x+1)^(4))`C. `(2)/((x+2)^(2))+(4)/((x+1)^(3))+(7)/((x+1)^(4))`D. `(4)/((x+1)^(2))+(5)/((x+1)^(3))+(7)/((x+1)^(4))`
Answer» Given , `(2x^(2)+8x+13)/((x+1)^(4))` Let `y=x+1impliesx=y=-1` `=(2(y-1)^(2)+8(y-1)+13)/(y^(4))` `=(2y^(2)+2-4y+8y-8+13)/(y^(4))` `=(2y^(2)+4y+7)/(y^(4))=(2)/(y^(2))+(4)/(y^(3))+(7)/(y^(4))` `=(2)/((x+1)^(2))+(4)/((x+1)^(3))+(7)/((x+1)^(4))`.

Discussion

9.	Resolve `(x^(2)+x+1)/(x^(3)+1)` into partical fractions.A. `(1)/(3(x+1))+(x+1)/(3(x^(2)-x+1))`B. `(-1)/(3(x+1))+(2x+2)/(3(x^(2)-x+1))`C. `(1)/(3(x+1))+(2x+2)/(3(x^(2)-x+1))`D. None of these
Answer» `(x^(2)+x+1)/(x^(3)+1)=(A)/(x+1)+(Bx+C)/(x^(2)-x+1)`

Discussion

10.	If `(4x^(2)+5x+6)/(x^(2)(x+3))=(A)/(x)+(B)/(x^(2))+(C )/(x+3)`, then `2A+3B+4C=` __________.A. `10`B. `20`C. `30`D. `40`
Answer» `(4x^(2)+5x+6)/(x^(2)(x+3))=(A)/(x)+(B)/(x^(2))+(C )/(x+3)` `(4x^(2)+5x+6)/(x^(2)(x+3))=(Ax(x+3)+B(x+3)+Cx^(2))/(x^(2)(x+3))` Consider, `4x^(2)+5x+6=Ax(x+3)+B(x+3)+cx^(2)` Put `x=0`, `6=3BimpliesB=2` Put `x=-3`, `27=9CimpliesC=3` Comparing the coefficient of `x^(2)`, we have `A+C=4impliesA=1` `2A+3B+4C=2+6+12=20`.

Discussion

11.	Find the constants `a,b,c` and `d`, respectively, if `(1)/(x^(4)-x)=(a)/(x)+(b)/(x-1)+(cx+d)/(x^(2)+x+1)`.A. `-1,(1)/(3),(-1)/(2),(-5)/(6)`B. `-1,(1)/(3),(-1)/(2),(5)/(6)`C. `1,(1)/(3),(1)/(2),(5)/(6)`D. None of these
Answer» `(i)` Simplify L.H.S and R.H.s `(ii)` Put `x=0` and `1` and obtain the values of `a` and `b`. `(iii)` Compare the like terms and obtain the values of `c` and `d`.

Discussion

12.	If `(3x^(2)+14x+10)/(x^(2)(x+2))=(A)/(x)+(B)/(x^(2))+(C )/(x+2)`, then `A`, `B` and `C`, respectively are _______.A. `(9)/(2)`, `-5`, `(3)/(2)`B. `(9)/(2)`, `5`, `(-3)/(2)`C. `(9)/(2)`,`(3)/(2)`, `-5`D. `(-9)/(2)`,`(-3)/(2)`, `5`
Answer» `(i)` Simplify L.H.S and R.H.S by taking L.C.M. `(ii)` Put `x=0` and `-2` and obtain the values of `A` and `B`. `(iii)` Comparing the like terms and obtain the value of `C`.

Discussion

13.	If `(2x-1)/((x+1)(x^(2)-1))=(A)/(x-1)+(B)/(x+1)+(C )/((x+1)^(2))`, then `A`, `B` ,`C`, respectively are _______.A. `(1)/(4)`, `(-1)/(4)`, `(3)/(2)`B. `(1)/(4)`, `(1)/(4)`, `(3)/(2)`C. `(1)/(4)`, `(-5)/(2)`, `(5)/(4)`D. `(1)/(4)`, `(5)/(2)`, `(5)/(4)`
Answer» `(i)` Simplify L.H.S and R.H.S by taking L.C.M. `(ii)` Compare the like terms and obtain the required values.

Discussion

14.	Resolve `(10)/(x^(2)-25)` into partical fractions.A. `(1)/(x-5)-(1)/(x+5)`B. `(1)/(x-5)+(2)/(x+5)`C. `(1)/(x+5)+(1)/(x-5)`D. `(1)/(x-5)-(2)/(x+5)`
Answer» Let `(10)/(x^(2)-25)=(A)/(x-5)+(B)/(x+5)` `(10)/(x^(2)-25)=(A(x+5)+B(x-5))/((x-5)(x+5))` Consider, `A(x+5)+B(x-5)=10` Put `x=5`, `10A=10impliesA=1` Put `x=-5`, `-10B=10impliesB=-1` `:. (10)/(x^(2)-5)=(1)/(x-5)-(1)/(x+5)`

Discussion

15.	Resolve `(2x)/(3(x-1)(x-3))` into partical fractions.A. `(1)/(x+3)-(1)/(3(x+1))`B. `(1)/(x-3)-(1)/(x+1)`C. `(1)/(x-3)-(1)/(3(x+1))`D. `(1)/(x-3)-(2)/(3(x-1))`
Answer» Let `((2x)/(3))/((x-1)(x-3))=(A)/((x-1))+(B)/((x-3))` `((2x)/(3))/((x-1)(x-3))=(A(x-3)+B(x-1))/((x-1)(x-3))` Consider , `A(x-3)+B(x-1)=(2x)/(3)` Put `x=3`, `2B=2impliesB=1`. Put `x=1`, `-2A=(2)/(3)impliesA=-(1)/(3)` `:. (2x)/(3(x-1)(x-3))=(1)/(x-3)-(1)/(3(x-1))`

Discussion

16.	Resolve `(3x+1)/((x-1)^(2))` into partical fractions.A. `(4)/((x-1))-(3)/((x-1)^(2))`B. `(3)/((x-1))-(4)/((x-1)^(2))`C. `(3)/((x-1)^(2))-(3)/((x-1)^(2))`D. `(3)/((x-1))+(4)/((x-1)^(2))`
Answer» `(3x+1)/((x-1)^(2))=(A)/(x-1)+(B)/((x-1)^(2))`.

Discussion

17.	Resolve `(2x^(2)+3)/(x^(4)+8x^(2)+15)` into partical fractions.A. `(3)/(2(x^(2)+3))+(5)/(2(x^(2)+5))`B. `(3)/(2(x^(2)-3))+(5)/(2(x^(2)+5))`C. `(-3)/(2(x^(2)+3))+(7)/(2(x^(2)+5))`D. `(7)/(2(x^(2)+3))-(3)/(2(x^(2)+5))`
Answer» `(2x^(2)+3)/(x^(4)+8x^(2)+15)=(Ax+B)/(x^(2)+5)+(Cx+D)/(x^(2)+3)`

Discussion

18.	Resolve `(1)/(x^(4)-3x^(2)-4)` into partical fractions.A. `(1)/(5(x^(2)-4))+(1)/(5(x^(2)+1))`B. `(1)/(5(x^(2)-4))-(1)/(5(x^(2)+1))`C. `(1)/(4(x^(2)+4))-(1)/(4(x^(2)+1))`D. `(1)/(4(x^(2)+4))+(1)/(4(x^(2)+1))`
Answer» `(1)/(x^(4)-3x^(2)-4)=(Ax+B)/(x^(2)-4)+(Cx+D)/(x^(1)+1)`.

Discussion

19.	Resolve `(3x+5)/(x^(2)+8x-20)` into partical fractions.A. `(11)/(24(x-2))+(25)/(24(x+10))`B. `(11)/(6(x-2))+(25)/(6(x+10))`C. `(11)/(12(x+2))+(25)/(12(x-10))`D. `(11)/(12(x-2))+(25)/(12(x+10))`
Answer» `(3x+5)/(x^(2)+8x-20)=(A)/(x+10)+(B)/(x-2)`.

Discussion

20.	Resolve `(3x-5)/(x^(2)+3x+2)` into partical fractions.A. `(7)/(x+2)-(5)/(x+1)`B. `(-8)/(x+2)-(11)/((x+1))`C. `(11)/(x+2)-(8)/(x+1)`D. `(7)/(x+2)+(5)/(x+1)`
Answer» `(3x-5)/(x^(2)+3x+2)=(A)/(x+1)+(B)/(x+2)`.

Discussion

21.	Resolve `(2x-5)/((x+2)(x^(2)-x+5))` into partial fractions.
Answer» Let `(2x-5)/((x+2)(x^(2)-x+5))=(A)/(x+2)+(Bx+C)/(x^(2)-x+5)` `implies2x-5=A(x^(2)-x+5)+(Bx+C)(x+2)`………..`(1)` Put `x=-2` in Eq. `(1)` `implies-9=A(11)+0` `A=(-9)/(11)` Again put `x=0` in Eq. `(1)`, we have `-5=5A+2C` `-5=5xx(-9)/(11)+2C` `impliesC=(-5)/(11)` Comparing the coefficients of `x^(2)` on both sides of Eq. `(1)`, we have `A+B=0` `B=-A=(9)/(11)` `:.(2x-5)/((x+2)(x^(2)-x+5))=(-9)/(11(x+2))+((9)/(11)x-(5)/(11))/(x^(2)-x+5)=(1)/(11)[(9x-5)/(x^(2)-x+5)-(9)/(x+2)]`

Discussion

22.	Resolve `(x)/((x+1)(x-1)^(2))` into partical fractions.A. `(1)/(2(x-1)^(2))+(1)/(4(x-1))+(1)/(4(x+1))`B. `(-1)/(4(x+1))+(1)/(4(x-1))+(1)/(2(x-1)^(2))`C. `(-1)/(4(x-1))+(1)/(4(x+1))+(1)/(2(x-1)^(2))`D. None of these
Answer» `(x)/((x+1)(x-1)^(2))=(A)/(x+1)+(B)/(x-1)+(C )/((x-1)^(2))`.

Discussion

23.	Resolve `(1)/(x^(2)-(a+b)x+ab)` into partical fractions.A. `(1)/(a+b)[(1)/(x-a)+(1)/(x-b)]`B. `(1)/(a+b)[(1)/(x-a)-(1)/(x-b)]`C. `(1)/(a-b)[(1)/(x-a)+(1)/(x-b)]`D. `(1)/(a-b)[(1)/(x-a)-(1)/(x-b)]`
Answer» `(1)/(x^(2)-(a+b)x+ab)=(A)/(x-a)+(B)/(x-b)`.

Discussion

24.	Resolve `(x+1)/(x^(2)-4)` into partical fractions.A. `(3)/(2(x-2))+(1)/(2(x+2))`B. `(3)/(2(x-2))-(1)/(2(x+2))`C. `(3)/(4(x-2))+(1)/(4(x+2))`D. `(3)/(4(x-2))-(1)/(4(x+2))`
Answer» `(x+1)/(x^(2)-4)=(A)/(x+2)+(B)/(x-2)`.

Discussion

25.	Resolve `(x-b)/(x^(2)+(a+b)x+ab)` into partical fractions.A. `(2a)/((a+b)(x+a))-(2b)/((a+b)(x+b))`B. `(a+b)/((a-b)(x+a))+(2b)/((a-b)(x+b))`C. `(a+b)/((a-b)(x+a))-(2b)/((a-b)(x+b))`D. None of these
Answer» `(x-b)/(x^(2)+(a+b)x+ab)=(A)/(x+a)+(B)/(x+b)`.

Discussion

26.	Resolve `(x+2)/(x^(2)-2x-15)` into partical fractions.A. `(7)/(8(x-5))+(1)/(8(x+3))`B. `(8)/(7(x-5))+(1)/(7(x+3))`C. `(5)/(8(x-5))+(1)/(8(x+3))`D. None of these
Answer» `(x+2)/(x^(2)-2x-15)=(A)/(x-5)+(B)/(x+3)`.

Discussion

27.	Resolve `(x-1)/(x^(3)-3x^(2)+2x)` into partical fractions.A. `(1)/((x-2))-(1)/(2x)`B. `(1)/(2(x-2))-(1)/(2x)`C. `(1)/((x-2))+(1)/(x-1)+(1)/(2x)`D. `(1)/((x-2))-(1)/(x-1)+(1)/(2x)`
Answer» `(i) x^(3)-3x^(2)+2x=x(x-1)(x-2)`. `(ii)(x-1)/((x^(3)-3x^(2)+2x))=(A)/(x)+(B)/(x-1)+(C )/(x-2)`.

Discussion

28.	Resolve `(3x^(2)+2x+4)/((x-1)(x^(2)-4))` into partical fractions.A. `(5)/(x-2)+(1)/(x-1)+(1)/(x+2)`B. `(5)/(x-2)+(2)/(x-1)+(1)/(x+2)`C. `(5)/(x-2)+(2)/(x-1)-(1)/(x+2)`D. `(5)/(x-2)-(3)/((x-1))+(1)/((x+2))`
Answer» `(3x^(2)+2x+4)/((x-1)(x^(2)-4))=(A)/(x-1)+(B)/(x-2)+(C )/(x+2)`.

Discussion

29.	Resolve `(2x+1)/(x^(2)-2x-8)` into partical fractions.A. `(3)/(2(x-4))-(1)/(2(x+2))`B. `(3)/(2(x-4))+(1)/(2(x+2))`C. `(1)/(2(x-4))-(3)/(2(x+2))`D. None of these
Answer» `(2x+1)/(x^(2)-2x-8)=(A)/(x-4)+(B)/(x+2)`.

Discussion

30.	Resolve `(x^(2)-x+1)/(x^(3)-1)` into partical fractions.A. `(1)/(3(x-1))+(2x-2)/(3(x^(2)+x+1))`B. `(1)/(3(x-1))-(2x-2)/(3(x^(2)+x+1))`C. `(1)/(2(x-1))+(x+2)/(2(x^(2)+x+1))`D. `(1)/(3(x-1))-(x-2)/(3(x^(2)+x+1))`
Answer» Split the denominator into factors and use the relaevant method to find its partial fraction.

Discussion

31.	If `(x)/((x-1)(x^(2)+1)^(2))=(P)/(x-1)+(Qx+R)/(x^(2)+1)+(Sx+T)/((x^(2)+1)^(2))`, then `P+Q-R-S+T=`____________.A. `(5)/(4)`B. `(3)/(2)`C. `(9)/(7)`D. `(8)/(9)`
Answer» `(x)/((x-1)(x^(2)+1)^(2))` `(P)/(x-1)+(Qx+R)/(x^(2)+1)+(Sx+T)/((x^(2)+1)^(2))` Consider, `x=P(x^(2)+1)^(2)+(Qx+R)(x^(2)+1)(x-1)+(Sx+T)(x-1)` Put `x=1`, `implies4P=1impliesP=(1)/(4)` Equation the coefficient of `x^(4)`, the coefficient of `x^(3)`, constant term and the coefficient of `x^(2)` from both sides. `P+Q=0`, i.e., `P=-Q:.Q=-(1)/(4)` `-Q+R=0`, i.e., `Q=R`, `:. R=(-1)/(4)` `P-R-T=0`, i.e., `T=P-R` `:.T=(1)/(2)` `2P+Q-R+S=0` That is, `S=-2P-(-1)/(2)` `P+Q-R-S+T=(1)/(4)-(1)/(4)+(1)/(4)+(1)/(2)+(1)/(2)=(5)/(4)`

Discussion

32.	Resolve `(2x^(2)+3x+18)/((x-2)(x+2)^(2))` into partical fractions.A. `(2)/((x+2))-(5)/((x-1)^(2))`B. `(2)/(x-2)+(1)/((x+2))+(3)/((x+2)^(2))`C. `(2)/(x-2)-(5)/((x+2)^(2))`D. `(2)/(x-2)-(1)/((x+2))+(3)/((x+2)^(2))`
Answer» `(2x^(2)+3x+18)/((x-2)(x+2)^(2))=(A)/(x-2)+(B)/(x+2)+(C )/((x+2)^(2))`.

Discussion

33.	If `(9x-13)/(x^(2)-2x-15)=(A)/(x+3)+(B)/(x-5)`, then `A+B` is ________.A. `9`B. `13`C. `12`D. `8`
Answer» Given, `(9x-13)/(x^(2)-2x-15)=(A)/(x+3)+(B)/(x-5)` Consider, `9x-13=A(x-5)+B(x+3)` `9x-13=Ax-5A+Bx+3B` Comparing the coefficients of `x`, we get `A+B=9`.

Discussion

34.	If `(1)/((1-x)(1-2x)(1-3x))=(A)/((1-x))+(B)/((1-2x))+(C )/((1-3x))`, then `A+B+C=`________.A. `0`B. `1`C. `-1`D. `2`
Answer» `(1)/((1-x)(1-2x)(1-3x))=(A)/(1-x)+(B)/(1-2x)+(C )/(1-3x)` `=(A(1-2x)(1-3x)+B(1-3x)(1-x)+C(1-x)(1-2x))/((1-x)(1-2x)(1-3x))` Consider, `A(1-2x)(1-3x)+B(1-3x)(1-x)+C(1-x)(1-2x)=1` Comparing constant terms, we get `A+B+C=1`

Discussion

35.	Resolve `(x+1)/(x(x-1)(x+3))` into partical fractions.A. `(-1)/(3x)+(1)/(2(x-1))-(1)/(6(x+3))`B. `(1)/(3x)+(1)/(2(x-1))-(1)/(6(x+3))`C. `(1)/(3x)-(1)/(2(x-1))+(1)/(6(x+3))`D. `(1)/(2x)-(1)/(3(x-1))+(1)/(6(x+3))`
Answer» `(x+1)/(x(x-1)(x+3))=(A)/(x)+(B)/(x-1)+(C )/(x+3)`.

Discussion

36.	Resolve `(5)/((x+2)(x+3))` into partical fractions.A. `5((1)/(x+2)+(1)/(x+3))`B. `5((1)/(x+2)-(1)/(x+3))`C. `10((1)/(x+2)-(1)/(x+3))`D. `10((1)/(x+2)+(1)/(x+3))`
Answer» Let `(5)/((x+2)(x+3))=(A)/((x+2))+(B)/((x+3))` `(5)/((x+2)(x+3))=(A(x+3)+B(x+2))/((x+2)(x+3))` Consider `A(x+3)+B(x+2)=5` If `x=-3`, `-B=5impliesB=-5` If `x=-2`, `A=5`. `:.(5)/((x+2)(x+3))=(5)/(x+2)-(5)/(x+3)`.

Discussion

37.	Resolve `(1)/(x^(2)-9)` into partical fractions.A. `(1)/(3(x-3))-(1)/(3(x+3))`B. `(1)/(2(x-3))-(3)/(2(x+3))`C. `(1)/(6(x-3))-(1)/(6(x+3))`D. `(1)/(6(x-3))+(1)/(6(x+3))`
Answer» `(1)/(x^(2)-9)=(A)/(x-3)+(B)/(x+3)`.

Discussion

38.	Resolve `(2x+3)/(x^(2)-6x+5)` into partical fractions.A. `(1)/(4)((13)/(x-5)-(5)/(x-1))`B. `(5)/(x-5)-(13)/(4(x-1))`C. `(13)/(5(x-1))-(4)/(5(x-5))`D. `(5)/(x-5)-(4)/((x-1))`
Answer» `(2x+3)/(x^(2)-6x+5)=(A)/((x-5))+(B)/((x-1))`.

Discussion

39.	Resolve `(1)/(x^(2)-7x+12)` into partical fractions.A. `(1)/(x-4)-(1)/(x-3)`B. `(1)/(x-3)+(1)/(x-4)`C. `(2)/(x-4)-(1)/(x-3)`D. `(1)/(x+3)-(1)/(x+4)`
Answer» `(1)/(x^(2)-7x+12)=(1)/((x-3)(x-4))` Let `(1)/((x-3)(x-4))=(A)/(x-3)+(B)/(x-4)`…..`(1)` `(1)/((x-3)(x-4))=(A(x-4)+B(x-3))/((x-3)(x-4))` Consider , `A(x-4)+B(x-3)=1` Put `x=4`, we get `B=1` Put `x=3`, we get `-A=1` `implies A=-1` Substitute these value in Eq. `(1)`, we get `(1)/((x-3)(x-4))=(1)/(x-4)-(1)/(x-3)`.

Discussion

40.	Resolve `(4x^(2)+3x+2)/((x-4)^(3))` into partical fractions.A. `(25)/(4(x-4))+(59)/(2(x-4))+(78)/(x-4)^(3)`B. `(25)/(4(x-4))-(69)/(2(x-4)^(2))+(78)/(x-4)^(3)`C. `(35)/(4(x-4))+(69)/(2(x-4)^(2))+(78)/(x-4)^(3)`D. `(4)/(x-4)+(35)/((x-4)^(2))+(78)/(x-4)^(3)`
Answer» `(4x^(2)+3x+2)/((x-4)^(3))=(A)/(x-4)+(B)/((x-4)^(2))+(C )/((x-4)^(3))`.

Discussion

41.	Resolve `(x^(2)+4x+6)/((x^(2)-1)(x+3))` into partical fractions.A. `(11)/(8(x-1))-(3)/(21(x-1))+(3)/(8(x+3))`B. `(11)/(8(x-1))-(3)/(4(x-1))+(3)/(8(x+3))`C. `(11)/(4(x+1))-(3)/(8(x+1))+(3)/(8(x+3))`D. `(11)/(8(x-1))-(3)/(4(x+1))+(3)/(8(x+3))`
Answer» `(x^(2)+4x+6)/((x^(2)-1)(x+3))=(A)/(x-1)+(B)/(x+1)+(C )/(x+3)`.

Discussion

42.	Resolve `(x)/((x-2)(x^(2)+3)^(2))` into partial fractions.A. `(1)/(49)[(2)/(x-2)-(2x+4)/(x^(2)+3)+(12-2x)/((x^(2)+3)^(2))]`B. `(1)/(49)[(2)/(x-2)-(2x+4)/(x^(2)+3)-(12-2x)/((x^(2)+3)^(2))]`C. `(1)/(49)[(2)/(x-2)+(2x+4)/(x^(2)+3)-(12-2x)/((x^(2)+3)^(2))]`D. `(1)/(49)[(2)/(x-2)-(2x+4)/(x^(2)+3)+(21-14x)/((x^(2)+3)^(2))]`
Answer» Let `(x)/((x-2)(x^(2)+3)^(2))=(A)/(x-2)+(Bx+C)/(x^(2)+3)+(Dx+E)/((x^(2)+3)^(2))` Consider, `x=A(x^(2)+3)^(2)+(Bx+C)(x-2)(x^(2)+3)+(Dx+E)(X-2)` Put `x=2`, we get `A=(2)/(49)` Comparing the coefficients of `x^(4)`, `x^(3)`, `x^(2)` and costant terms , we get `A+B=0implies:.B=-(2)/(49)` `-2B+C=0impliesC=-(4)/(49)` `6A+3B-2C+D=0` `implies:.D=(-14)/(49)` and `-6C-2E+9A=0` `E=(21)/(49)` `(x)/((x-2)(x^(2)+3)^(2))` `=((2)/(49))/(x-2)+((-2)/(49)x-(4)/(49))/(x^(2)+3)+((-14)/(49)x+(21)/(49))/((x^(2)+3)^(2))` `=(2)/(49(x-2))-(2x+4)/(49(x^(2)+3))+(21-14x)/(49(x^(2)+3)^(2))`

Discussion

43.	Resolve `(2x+1)/((x+3)(x^(2)+1)^(2))` into partial fractions.
Answer» Let, `(2x+1)/((x+3)(x^(2)+1)^(2))=(A)/(x+3)+(Bx+C)/(x^(2)+1)+(Dx+E)/((x^(2)+1)^(2))` `implies2x+1=A(x^(2)+1)^(2)+(Bx+C)(x+3)(x^(2)+1)+(Dx+E)(x+3)`………`(1)` Put `x=-3` in Eq. `(1)`, we have `-5=100AimpliesA=(-1)/(20)` Comparing the coefficients of `x^(4)` on either sides of Eq. `(1)`, we have `0=A+BimpliesB=(1)/(20)` Compairng the coefficients of `x^(3)` on either sides of Eq. `(1)`, we have `0=3B+CimpliesC=(-3)/(20)` Put `x=0` in Eq. `(1)`, we have `implies1=A+3C+3Eimplies3E=1+(1)/(20)+(9)/(20)` `impliesE=(1)/(2)` By putting `x=1` in Eq. `(1)`, we have `3=4A+8B+8C+4D+4E` `3=(-4)/(20)+(8)/(20)+8((-3)/(20))+4D+((1)/(2))` `3+(4)/(20)-(8)/(20)+(24)/(20)-2=4D` `D=(2)/(4)=(1)/(2)` `:.(2x+1)/((x+3)(x^(2)+1)^(2))=((-1)/(20))/(x+3)+((x)/(20)-(3)/(20))/(x^(2)+1)+((1)/(2)x+(1)/(2))/((x^(2)+1)^(2))` `=(-1)/(20(x+3))+((x-3))/(20(x^(2)+1))+((x+1))/(2(x^(2)+1)^(2))`

Discussion

44.	Resolve `(1)/(x^(2)-7x-18)` into partical fractions.A. `(1)/(11)((1)/(x-9)-(1)/(x+2))`B. `(1)/(11)((1)/(x-9)+(1)/(x+2))`C. `(1)/(11)((1)/(x+9)-(1)/(x-2))`D. `(1)/(11)((1)/(x+9)+(1)/(x+2))`
Answer» `(1)/(x^(2)-7x-18)=(A)/(x-9)+(B)/(x+2)`.

Discussion

45.	Resolve `(3x^(2)-3x-11)/((x+3)(3x+4)^(2))` into partial fractions.A. `(1)/(x+3)+(2)/(3x+4)-(1)/((3x+4)^(2))`B. `(1)/(x+3)-(2)/(3x+4)-(1)/((3x+4)^(2))`C. `(1)/(x+3)+(2)/(3x+4)-(1)/(2(3x+4)^(2))`D. None of these
Answer» Let, `(3x^(2)-3x-11)/((x+3)(3x+4)^(2))=(A)/(x+3)+(B)/(3x+4)+(C )/((3x+4)^(2))` Consider `3x^(2)-3x-11=A(3x+4)^(2)+B(x+3)(3x+4)+C(x+3)` `=A(9x^(2)+16+24x)+B(3x^(2)+13x+12)+C(x+3)` Comparing coefficient of `x^(2)`, coefficient of `x` and constant terms, we get, `9A+3B=3`.......`(1)` `24A+13B+C=-3`.........`(2)` `16A+12B+3C=-11`.......`(3)` Solving Eqs. `(1)`, `(2)` and `(3)`, we get `A=1`, `B=-2`, `C=-1` `:.(3x^(2)-3x-11)/((x+3)(3x+4)^(2))=-(1)/(x+3)-(2)/(3x+4)-(1)/((3x+4)^(2))`

Discussion

46.	Resolve `(x^(2)+x+1)/((x-1)^(3))` into partical fractions.A. `(1)/(x-1)+(1)/((x-1)^(2))+(1)/((x-1)^(3))`B. `(1)/((x-1))+(2)/((x-1)^(2))+(1)/((x-1)^(3))`C. `(1)/(x-1)+(3)/((x-1)^(2))+(3)/((x-1)^(3))`D. `(2)/(x-1)+(3)/((x-1)^(2))+(3)/((x-1)^(3))`
Answer» `(x^(2)+x+1)/((x-1)^(3))=(A)/(x-1)+(B)/((x-1)^(2))+(C )/((x-1)^(3))`

Discussion

47.	Resolve `(1)/(x^(2)+x+42)` into partical fractions.A. `(1)/(13(x-6))+(1)/(13(x+7))`B. `(1)/((x-7))+(1)/((x-6))`C. `(1)/((x-7))-(1)/((x-6))`D. `(1)/(13(x-6))-(1)/(13(x+7))`
Answer» `(1)/(x^(2)+x-42)=(A)/(x+7)+(B)/(x-6)`.

Discussion

48.	Resolve `(1)/(x^(2)-5x+6)` into partical fractions.A. `(1)/(x-3)-(1)/(x-2)`B. `(1)/(x-2)+(1)/(x-3)`C. `(1)/(x-3)+(1)/(x-2)`D. `(2)/(x-3)+(2)/(x-2)`
Answer» `(x+2)/(x^(2)-5x+6)=(A)/(x-3)+(B)/(x-2)`.

Discussion

49.	Resolve `(2x^(2)-5x+7)/((x+1)^(2)(x+3)(2x+1))` into partial fractions.
Answer» Let `(2x^(2)-5x+7)/((x+1)^(2)(x+3)(2x+1))=(A)/(x+1)+(B)/((x+1)^(2))+(C )/(x+3)+(D)/(2x+1)` `implies2x^(2)-5x+7=A(x+1)(x+3)(2x+1)+B(x+3)(2x+1)+C(x+1)^(2)(2x+1)+D(x+1)^(2)(x+3)`…………..`(1)` Substituting `x=-1` in Eq. `(1)`, we have `2(-1)^(2)-5(-1)+7=A(0)+B(-1+3)(-2+1)+C(0)+D(0)14=-2B` `B=-7` Substituting `x=-3` in Eq. `(1)` , we get `40=A(0)+B(0)+C(-20)+D(0)-20C=40` `C=-2` Substituting `x=-(1)/(2)` in Eq. `(1)` , we have `10=(5)/(8)DimpliesD=16` Substituting `x=0`, we have `7=3A+3B+C+3D` Substituting the values of `B,C,D` in the above equation , we get `A=-6` `:.(2x^(2)-5x+7)/((x+1)^(2)(x+3)(2x+1))=(-6)/(x+1)+(-7)/((x+1)^(2))+(-2)/(x+3)+(16)/(2x+1)`

Discussion

50.	Resolve `(2x^(2)+5x-1)/(x^(2)-3x-10)` into partial fractions.
Answer» Given, `(2x^(2)+5x-1)/(x^(2)-3x-10)` We can clearly notice buut the given fraction is an improper fraction. So dividing the numerator by the denominator, we can express `(2x^(2)+5x-1)/(x^(2)-3x-10)` as `(11x+19)/(x^(2)-3x-10)` Let `(11x+19)/((x+2)(x-5))=(A)/(x+2)+(B)/(x-5)` `11x+19=A(x-5)+B(x+2)`..........`(1)` Put `x=5` in Eq. `(1)implies55+19=A(0)+B(7)` `:.B=(74)/(7)` Again put `x=2` in Eq. `(1)implies22+19=A(7)+B(0)impliesA=(3)/(7)` `:.(2x^(2)+5x-1)/(x^(2)-3x-10)=2+(3)/(7(x+2))+(74)/(7(x-5))`.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Resolve `(3x+5)/((x+2)(3x-1))` into partial fractions.

Resolve `(ax-b)/((x+1)^(2))` into partical fractions.A. `(a)/(x+1)+(a+b)/((x+1)^(2))`B. `(a)/(x+1)+(a-b)/((x+1)^(2))`C. `(a)/(x+1)-(a-b)/((x+1)^(2))`D. `(a)/(x+1)-(a+b)/((x+1)^(2))`

Resolve `(3x^(2)+7)/(x^(4)-3x^(2)+2)` into partical fractions.A. `(10)/(x^(2)-2)+(5)/(x-1)-(5)/(x+1)`B. `(13)/(x^(2)-2)+(5)/(x+1)-(5)/(x-1)`C. `(5)/(x^(2)-2)+(10)/(x-1)-(10)/(x+1)`D. `(5)/(x-1)-(5)/(x+1)-(13)/(x^(2)-2)`

If `(x^(3))/((x-1)(x-2))=Ax+B+(C )/(x-1)+(D)/(x-2)`, then `A,B,C` and `D`, respectively are ____________.A. `1,3,1,8`B. `1,-1,3,8`C. `1,3,-1,8`D. `-1,-3,1,8`

Resolve `(1)/((x-4)(x^(2)+3))` into partical fractions.A. `(1)/(19)[(1)/(x-4)+(x+4)/(x^(2)+3)]`B. `(1)/(19)[(1)/(x-4)+(x+3)/(x^(2)+3)]`C. `(1)/(19)[(1)/(x-4)+(x+3)/(x^(2)+3)]`D. `(1)/(19)[(1)/(x-4)-(x+4)/(x^(2)+3)]`

Resolve `(6x^(2)-14x+6)/(x(x-1)(x-2))` into partical fractions.A. `(2)/(x)+(3)/(x-1)+(1)/(x-2)`B. `(3)/(x)+(2)/(x-1)+(1)/(x-2)`C. `(1)/(x)+(2)/(x-1)+(3)/(x-2)`D. `(1)/(x)+(3)/(x-1)+(2)/(x-2)`

Resolve `(2x^(2)+8x+13)/((x+1)^(4))` into partical fractions.A. `(2)/((x+1)^(2))+(5)/((x+1)^(3))+(7)/((x+1)^(4))`B. `(1)/((x+1)^(2))+(5)/((x+1)^(3))+(7)/((x+1)^(4))`C. `(2)/((x+2)^(2))+(4)/((x+1)^(3))+(7)/((x+1)^(4))`D. `(4)/((x+1)^(2))+(5)/((x+1)^(3))+(7)/((x+1)^(4))`

Resolve `(x^(2)+x+1)/(x^(3)+1)` into partical fractions.A. `(1)/(3(x+1))+(x+1)/(3(x^(2)-x+1))`B. `(-1)/(3(x+1))+(2x+2)/(3(x^(2)-x+1))`C. `(1)/(3(x+1))+(2x+2)/(3(x^(2)-x+1))`D. None of these

If `(4x^(2)+5x+6)/(x^(2)(x+3))=(A)/(x)+(B)/(x^(2))+(C )/(x+3)`, then `2A+3B+4C=` __________.A. `10`B. `20`C. `30`D. `40`

Find the constants `a,b,c` and `d`, respectively, if `(1)/(x^(4)-x)=(a)/(x)+(b)/(x-1)+(cx+d)/(x^(2)+x+1)`.A. `-1,(1)/(3),(-1)/(2),(-5)/(6)`B. `-1,(1)/(3),(-1)/(2),(5)/(6)`C. `1,(1)/(3),(1)/(2),(5)/(6)`D. None of these

If `(3x^(2)+14x+10)/(x^(2)(x+2))=(A)/(x)+(B)/(x^(2))+(C )/(x+2)`, then `A`, `B` and `C`, respectively are _______.A. `(9)/(2)`, `-5`, `(3)/(2)`B. `(9)/(2)`, `5`, `(-3)/(2)`C. `(9)/(2)`,`(3)/(2)`, `-5`D. `(-9)/(2)`,`(-3)/(2)`, `5`

If `(2x-1)/((x+1)(x^(2)-1))=(A)/(x-1)+(B)/(x+1)+(C )/((x+1)^(2))`, then `A`, `B` ,`C`, respectively are _______.A. `(1)/(4)`, `(-1)/(4)`, `(3)/(2)`B. `(1)/(4)`, `(1)/(4)`, `(3)/(2)`C. `(1)/(4)`, `(-5)/(2)`, `(5)/(4)`D. `(1)/(4)`, `(5)/(2)`, `(5)/(4)`

Resolve `(10)/(x^(2)-25)` into partical fractions.A. `(1)/(x-5)-(1)/(x+5)`B. `(1)/(x-5)+(2)/(x+5)`C. `(1)/(x+5)+(1)/(x-5)`D. `(1)/(x-5)-(2)/(x+5)`

Resolve `(2x)/(3(x-1)(x-3))` into partical fractions.A. `(1)/(x+3)-(1)/(3(x+1))`B. `(1)/(x-3)-(1)/(x+1)`C. `(1)/(x-3)-(1)/(3(x+1))`D. `(1)/(x-3)-(2)/(3(x-1))`

Resolve `(3x+1)/((x-1)^(2))` into partical fractions.A. `(4)/((x-1))-(3)/((x-1)^(2))`B. `(3)/((x-1))-(4)/((x-1)^(2))`C. `(3)/((x-1)^(2))-(3)/((x-1)^(2))`D. `(3)/((x-1))+(4)/((x-1)^(2))`

Resolve `(2x^(2)+3)/(x^(4)+8x^(2)+15)` into partical fractions.A. `(3)/(2(x^(2)+3))+(5)/(2(x^(2)+5))`B. `(3)/(2(x^(2)-3))+(5)/(2(x^(2)+5))`C. `(-3)/(2(x^(2)+3))+(7)/(2(x^(2)+5))`D. `(7)/(2(x^(2)+3))-(3)/(2(x^(2)+5))`

Resolve `(1)/(x^(4)-3x^(2)-4)` into partical fractions.A. `(1)/(5(x^(2)-4))+(1)/(5(x^(2)+1))`B. `(1)/(5(x^(2)-4))-(1)/(5(x^(2)+1))`C. `(1)/(4(x^(2)+4))-(1)/(4(x^(2)+1))`D. `(1)/(4(x^(2)+4))+(1)/(4(x^(2)+1))`

Resolve `(3x+5)/(x^(2)+8x-20)` into partical fractions.A. `(11)/(24(x-2))+(25)/(24(x+10))`B. `(11)/(6(x-2))+(25)/(6(x+10))`C. `(11)/(12(x+2))+(25)/(12(x-10))`D. `(11)/(12(x-2))+(25)/(12(x+10))`

Resolve `(3x-5)/(x^(2)+3x+2)` into partical fractions.A. `(7)/(x+2)-(5)/(x+1)`B. `(-8)/(x+2)-(11)/((x+1))`C. `(11)/(x+2)-(8)/(x+1)`D. `(7)/(x+2)+(5)/(x+1)`

Resolve `(2x-5)/((x+2)(x^(2)-x+5))` into partial fractions.

Resolve `(x)/((x+1)(x-1)^(2))` into partical fractions.A. `(1)/(2(x-1)^(2))+(1)/(4(x-1))+(1)/(4(x+1))`B. `(-1)/(4(x+1))+(1)/(4(x-1))+(1)/(2(x-1)^(2))`C. `(-1)/(4(x-1))+(1)/(4(x+1))+(1)/(2(x-1)^(2))`D. None of these

Resolve `(1)/(x^(2)-(a+b)x+ab)` into partical fractions.A. `(1)/(a+b)[(1)/(x-a)+(1)/(x-b)]`B. `(1)/(a+b)[(1)/(x-a)-(1)/(x-b)]`C. `(1)/(a-b)[(1)/(x-a)+(1)/(x-b)]`D. `(1)/(a-b)[(1)/(x-a)-(1)/(x-b)]`

Resolve `(x+1)/(x^(2)-4)` into partical fractions.A. `(3)/(2(x-2))+(1)/(2(x+2))`B. `(3)/(2(x-2))-(1)/(2(x+2))`C. `(3)/(4(x-2))+(1)/(4(x+2))`D. `(3)/(4(x-2))-(1)/(4(x+2))`

Resolve `(x-b)/(x^(2)+(a+b)x+ab)` into partical fractions.A. `(2a)/((a+b)(x+a))-(2b)/((a+b)(x+b))`B. `(a+b)/((a-b)(x+a))+(2b)/((a-b)(x+b))`C. `(a+b)/((a-b)(x+a))-(2b)/((a-b)(x+b))`D. None of these

Resolve `(x+2)/(x^(2)-2x-15)` into partical fractions.A. `(7)/(8(x-5))+(1)/(8(x+3))`B. `(8)/(7(x-5))+(1)/(7(x+3))`C. `(5)/(8(x-5))+(1)/(8(x+3))`D. None of these

Resolve `(x-1)/(x^(3)-3x^(2)+2x)` into partical fractions.A. `(1)/((x-2))-(1)/(2x)`B. `(1)/(2(x-2))-(1)/(2x)`C. `(1)/((x-2))+(1)/(x-1)+(1)/(2x)`D. `(1)/((x-2))-(1)/(x-1)+(1)/(2x)`

Resolve `(3x^(2)+2x+4)/((x-1)(x^(2)-4))` into partical fractions.A. `(5)/(x-2)+(1)/(x-1)+(1)/(x+2)`B. `(5)/(x-2)+(2)/(x-1)+(1)/(x+2)`C. `(5)/(x-2)+(2)/(x-1)-(1)/(x+2)`D. `(5)/(x-2)-(3)/((x-1))+(1)/((x+2))`

Resolve `(2x+1)/(x^(2)-2x-8)` into partical fractions.A. `(3)/(2(x-4))-(1)/(2(x+2))`B. `(3)/(2(x-4))+(1)/(2(x+2))`C. `(1)/(2(x-4))-(3)/(2(x+2))`D. None of these

Resolve `(x^(2)-x+1)/(x^(3)-1)` into partical fractions.A. `(1)/(3(x-1))+(2x-2)/(3(x^(2)+x+1))`B. `(1)/(3(x-1))-(2x-2)/(3(x^(2)+x+1))`C. `(1)/(2(x-1))+(x+2)/(2(x^(2)+x+1))`D. `(1)/(3(x-1))-(x-2)/(3(x^(2)+x+1))`

If `(x)/((x-1)(x^(2)+1)^(2))=(P)/(x-1)+(Qx+R)/(x^(2)+1)+(Sx+T)/((x^(2)+1)^(2))`, then `P+Q-R-S+T=`____________.A. `(5)/(4)`B. `(3)/(2)`C. `(9)/(7)`D. `(8)/(9)`

Resolve `(2x^(2)+3x+18)/((x-2)(x+2)^(2))` into partical fractions.A. `(2)/((x+2))-(5)/((x-1)^(2))`B. `(2)/(x-2)+(1)/((x+2))+(3)/((x+2)^(2))`C. `(2)/(x-2)-(5)/((x+2)^(2))`D. `(2)/(x-2)-(1)/((x+2))+(3)/((x+2)^(2))`

If `(9x-13)/(x^(2)-2x-15)=(A)/(x+3)+(B)/(x-5)`, then `A+B` is ________.A. `9`B. `13`C. `12`D. `8`

If `(1)/((1-x)(1-2x)(1-3x))=(A)/((1-x))+(B)/((1-2x))+(C )/((1-3x))`, then `A+B+C=`________.A. `0`B. `1`C. `-1`D. `2`

Resolve `(x+1)/(x(x-1)(x+3))` into partical fractions.A. `(-1)/(3x)+(1)/(2(x-1))-(1)/(6(x+3))`B. `(1)/(3x)+(1)/(2(x-1))-(1)/(6(x+3))`C. `(1)/(3x)-(1)/(2(x-1))+(1)/(6(x+3))`D. `(1)/(2x)-(1)/(3(x-1))+(1)/(6(x+3))`

Resolve `(5)/((x+2)(x+3))` into partical fractions.A. `5((1)/(x+2)+(1)/(x+3))`B. `5((1)/(x+2)-(1)/(x+3))`C. `10((1)/(x+2)-(1)/(x+3))`D. `10((1)/(x+2)+(1)/(x+3))`

Resolve `(1)/(x^(2)-9)` into partical fractions.A. `(1)/(3(x-3))-(1)/(3(x+3))`B. `(1)/(2(x-3))-(3)/(2(x+3))`C. `(1)/(6(x-3))-(1)/(6(x+3))`D. `(1)/(6(x-3))+(1)/(6(x+3))`

Resolve `(2x+3)/(x^(2)-6x+5)` into partical fractions.A. `(1)/(4)((13)/(x-5)-(5)/(x-1))`B. `(5)/(x-5)-(13)/(4(x-1))`C. `(13)/(5(x-1))-(4)/(5(x-5))`D. `(5)/(x-5)-(4)/((x-1))`

Resolve `(1)/(x^(2)-7x+12)` into partical fractions.A. `(1)/(x-4)-(1)/(x-3)`B. `(1)/(x-3)+(1)/(x-4)`C. `(2)/(x-4)-(1)/(x-3)`D. `(1)/(x+3)-(1)/(x+4)`

Resolve `(4x^(2)+3x+2)/((x-4)^(3))` into partical fractions.A. `(25)/(4(x-4))+(59)/(2(x-4))+(78)/(x-4)^(3)`B. `(25)/(4(x-4))-(69)/(2(x-4)^(2))+(78)/(x-4)^(3)`C. `(35)/(4(x-4))+(69)/(2(x-4)^(2))+(78)/(x-4)^(3)`D. `(4)/(x-4)+(35)/((x-4)^(2))+(78)/(x-4)^(3)`

Resolve `(x^(2)+4x+6)/((x^(2)-1)(x+3))` into partical fractions.A. `(11)/(8(x-1))-(3)/(21(x-1))+(3)/(8(x+3))`B. `(11)/(8(x-1))-(3)/(4(x-1))+(3)/(8(x+3))`C. `(11)/(4(x+1))-(3)/(8(x+1))+(3)/(8(x+3))`D. `(11)/(8(x-1))-(3)/(4(x+1))+(3)/(8(x+3))`

Resolve `(2x+1)/((x+3)(x^(2)+1)^(2))` into partial fractions.

Resolve `(1)/(x^(2)-7x-18)` into partical fractions.A. `(1)/(11)((1)/(x-9)-(1)/(x+2))`B. `(1)/(11)((1)/(x-9)+(1)/(x+2))`C. `(1)/(11)((1)/(x+9)-(1)/(x-2))`D. `(1)/(11)((1)/(x+9)+(1)/(x+2))`

Resolve `(3x^(2)-3x-11)/((x+3)(3x+4)^(2))` into partial fractions.A. `(1)/(x+3)+(2)/(3x+4)-(1)/((3x+4)^(2))`B. `(1)/(x+3)-(2)/(3x+4)-(1)/((3x+4)^(2))`C. `(1)/(x+3)+(2)/(3x+4)-(1)/(2(3x+4)^(2))`D. None of these

Resolve `(x^(2)+x+1)/((x-1)^(3))` into partical fractions.A. `(1)/(x-1)+(1)/((x-1)^(2))+(1)/((x-1)^(3))`B. `(1)/((x-1))+(2)/((x-1)^(2))+(1)/((x-1)^(3))`C. `(1)/(x-1)+(3)/((x-1)^(2))+(3)/((x-1)^(3))`D. `(2)/(x-1)+(3)/((x-1)^(2))+(3)/((x-1)^(3))`

Resolve `(1)/(x^(2)+x+42)` into partical fractions.A. `(1)/(13(x-6))+(1)/(13(x+7))`B. `(1)/((x-7))+(1)/((x-6))`C. `(1)/((x-7))-(1)/((x-6))`D. `(1)/(13(x-6))-(1)/(13(x+7))`

Resolve `(1)/(x^(2)-5x+6)` into partical fractions.A. `(1)/(x-3)-(1)/(x-2)`B. `(1)/(x-2)+(1)/(x-3)`C. `(1)/(x-3)+(1)/(x-2)`D. `(2)/(x-3)+(2)/(x-2)`

Resolve `(2x^(2)-5x+7)/((x+1)^(2)(x+3)(2x+1))` into partial fractions.

Resolve `(2x^(2)+5x-1)/(x^(2)-3x-10)` into partial fractions.