Could someone justify the following statement please. I'm having trouble visualizing what has been said here:

If by direct substitution of a given value c into a rational function is made and the following result occurs

$\displaystyle r(c)=\frac{p(c)}{q(c)}=\frac{0}{0}$

then it can be concluded that $\displaystyle (x-c)$ is a factor of both $\displaystyle p(x)$ and $\displaystyle q(x)$.

Anything to shed light here would be appreciated. Thanks.