Question

How do you express `(x^2 + 33)/(x^3 + x^2)` in partial fractions?

Answer 1

`(x^2+33)/(x^2(x+1)) = -33/x +33/x^2 +34/(x+1)`

Explanation:

`(x^2+33)/(x^2(x+1)) = A/x +B/x^2 +C/(x+1)`

`x^2+33 = A(x(x+1))+B(x+1)+Cx^2`

`x^2+33 = Ax^2+Ax+Bx+B+Cx^2`

`1=A+C, 0=A+B, 33=B`

`A=-33, B=33, C=34`

`(x^2+33)/(x^2(x+1)) = -33/x +33/x^2 +34/(x+1)`