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 $q(s)=0$ .