Suppose $f$  is a rational function with polynomial functions $p(x)$ and $q(x)$ so that for any $x \in D_f$, it domain, with $q(x) \ne 0$, $f(x) = \frac {p(x)} {q(x)}$.

Definition: A pole of $f$ is a number $s$ where $q(s)=0$ .