I've been trying to read about partial fraction expansion of rational function.
Is the following statement equivalent to the uniqueness+existence of partial function expansion?:
Let $\mathbb{F}$ be an algebraically closed field and let $D=\{\frac{p}{q}~:~p,q\in\mathbb{F}[x],~\deg(p)\leq\deg(q)\}$. Consider $D$ as a linear space above $\mathbb{F}$. Then the set $\{(x-a)^{n}~:~a\in\mathbb{F},~n\leq0\}$ is a basis for $D$.