This is essentially a definition question.
Given a rational function $\frac{p(x)}{q(x)}$, what would the $x^k$ coefficient of this rational function mean (in particular for the negative $k$'s). Is there some sort of expansion $\frac{p(x)}{q(x)} = \sum_{-\infty}^\infty a_kx^k$ where one would say $a_k$ is the coefficient of $x^k$?
How would you find the coefficient? A very simple rational function would be $\frac{(x - 1)}{(x - 2)(x - 3)}$. How would you find the $x^{-1}$ coefficient of this?
Thanks for any help and clarifications.