Question

How do you write the partial fraction decomposition of the rational expression `(x^3 + x) /(x^2 + x + 1)^2`?

Answer 1

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

Explanation:

Using the Ansatz
`(x^3+x)/(x^2+x+1)^2=(Ax+B)/(x^2+x+1)^2+(Cx+D)/(x^2+x+1)`
we get `A=1,B=-1,C=1,D=1`