# Writing beta function in terms of gamma functions (by substitution)

I'm going over my note and try to write the Beta function in terms of gamma functions. However, I just can't get (1.73) from (1.72).

Even if I substitute t/(1-t) with u, I can't remove t. Can anyone shed some light on this? Thanks.

Hint: If $$u = \frac{t}{1-t}$$, then $$u(1-t)=t$$, that is, \begin{align*} u-ut &=t \\ \Rightarrow u &= ut+t \\ \Rightarrow u &=t(1+u).\end{align*} So $$t= \frac{u}{1+u}$$. Try substituting this now.