# partial fraction decomposition third power

I would like to use partial fraction decomposition on: $$\frac{x+1}{x^4+x}$$. The denominator can be broken into $$x(x^3+1)$$. I'm just not sure how to deal with the $$x^3+1$$ part. Do I put something like: $$Ax^2+Bx+C$$ on top? That would lead to a step looking like this: $$\frac{Ax^2+Bx+C}{x^3+1}+\frac{D}{x}$$. Or, is there something else I need to do?

• $x^3+1$ is divisible by $x-1$ – Tito Eliatron Jan 14 at 20:51
• @TitoEliatron, I think you meant $x+1$. – RobPratt Jan 14 at 20:54
• Yeah, it was a misprint. Thanks. – Tito Eliatron Jan 14 at 20:59

$$\frac{x+1}{x^4+x}=\frac{x+1}{x(x+1)(x^2-x+1)}=\frac{1}{x(x^2-x+1)}=\frac{1}{x}-\frac{x+1}{x^2-x+1}$$