TITLE: partial fraction decomposition third power
QUESTION [0 upvotes]: 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?

REPLY [1 votes]: $$
\frac{x+1}{x^4+x}=\frac{x+1}{x(x+1)(x^2-x+1)}=\frac{1}{x(x^2-x+1)}=\frac{1}{x}-\frac{x+1}{x^2-x+1}
$$
{"set_name": "stack_exchange", "score": 0, "question_id": 3509250}