How do we show that

$\displaystyle \lim_{x \rightarrow \infty} \, \frac {e^x (x-1)!}{x!} = + \infty \, .$

I know that the factorial functionen approaches infinity faster than most other elementary functions e.g. $\displaystyle e^x$. But I am not sure how to think when we have a factorial function in both the nominator and denominator.