Question

How do you express `x^3/[x(x^2+2x+1)]` in partial fractions?

Answer 1

`x^3/(x(x^2+2x+1))=1-2/(x+1)+1/(x+1)^2`

Explanation:

This one is relatively simpler and need for detailed solution as given here, does not arise.

`x^3/(x(x^2+2x+1))=x^2/(x^2+2x+1)=(x^2+2x+1-(2x+1))/(x^2+2x+1)`

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

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

= `1-(2(x+1))/(x+1)^2+1/(x+1)^2` or

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