In deriving the MLE estimate for the population proportion of a binomially distributed rv I need to simplify the following expression involving the gamma function for $l,m,a,b \in \mathbb{N}$
$$ \frac{\Gamma(l+m)}{\Gamma(m)\Gamma(l)}\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}$$
which can be found on page 71 of Bishops machine learning text.
As I simply don't know which gamma identities to use here, I was wondering how bishop simplified the expression to
$$\frac{\Gamma(m+a+l+b)}{\Gamma(m+a)\Gamma(l+b)}$$