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

1.	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)]`

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

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