Resolve `(x^(3)-2x^(2)-13x-12)/(x^(2)-3x-10)` into partial fractions.

1.	Resolve `(x^(3)-2x^(2)-13x-12)/(x^(2)-3x-10)` into partial fractions.
Answer» On dividing we get `(x^(3)-2x^(2)-13x-12)/(x^(2)-3x-10)=(x+1)-(2)/((x^(2)-3x-10))` `Let (2)/((x^(2)-3x-10))=(2)/((x-5)(x+2))=(A)/(x-5)+(B)/(x+2)` then`, (2)/((x-5)(x+2))+(A(x+2)+B(x-5))/((x-5)(x+2))` or `2-= A(x+2)+B(x-5).` putting `(x-5)=0 or x=5 `in (ii) , we get `A=(2//7)` Putting `(x+2)=0 or x=-2`in (ii) , we get `B=(-2//7)` `therefore (2)/((x^(2)-3x-10))=(2)/(7(x-5))-(2)/(7(x+2)).` `"hence", (x^(3)-2x^(2)-13x-12)/(x^(2)-3x-10)=(x+1)-(2)/(7(x-5))+(2)/(7(x+2)).`

Discussion

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