Let $q$ be a polynomial of degree $n$ with distinct zeroes $z_1,\ldots,z_n$. Let $p$ be a polynomial of degree $n-2$ or less. Show that:
$\displaystyle\sum_{K=1}^{n} \operatorname{Res}\left(\frac{p}{q};z_k\right)=0$
I'm trying to think of ways to use the residue theorem, but I'm not sure how to proceed...any input would be appreciated!!