Sum of all residues of $P/Q$ are zero.

Question

Let $P(z)$ and $Q(z)$ be two polynomials with $deg(P)=m$ and $deg(Q)=m+2$. Prove that the sum of all residues of $P/Q$ are zero.

Here are my thoughts. I know and understand what the degree of a polynomial is, but are we really just looking at the values of the residues when $Q(z)$ has singularities?

Answer 1

Hint: Consider the integral around a very big circle. What can you say about $P(z)/Q(z)$ when $|z|$ is very large?