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

1.	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))`.

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

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