Let $\displaystyle f(z)=\frac{p(z)}{q(z)}$, where $\displaystyle p(z)$ and $\displaystyle q(z)$ are polynomials. Prove that the sum of multiplicities of all zeroes minus the sum of orders of all poles, including zeroes or poles at $\displaystyle \infty$, equals zero.

I am not sure how to prove this. I was thinking to use the argument principle somehow. However, could not figure out how. I need some hints on how this one. Thanks.