## how to prove this version of L'Hopital's rule

Please prove the following version of L'Hopital's rule.
Suppose that $f,g : (a,b) \rightarrow \Re$
are differentiable with
$g(x)$ and $g'(x)$ never equal to zero.
suppose also that:
$lim_{x \rightarrow b-} f(x) =0$
$lim_{x \rightarrow b-} g(x) =0$
$lim_{x \rightarrow b-} \frac{f'(x)}{g'(x)} = \infty$
then
$lim_{x \rightarrow b-} \frac{f(x)}{g(x)} = \infty$