sum of the residue at all poles of the rational function p/q is 0. We are given two polynomials p, q with deg(q)>1+deg(p). Show that the sum of the residue at all poles of the rational function p/q is 0. 
How do I go about solving this?

Hint: Let $\gamma_R$ be a circle of radius $R$ around 0 such that all zeros of $q$ lie inside $\gamma_R$. What can you say for $\int_{\gamma_R} \frac pq \, dz$ for $R \to \infty$? How can you connect this with the residue sum?
