Relation Between Beta and Gamma functions

[PLAGUE]

TL;DR

Proof of Beta Gamma function relation

So, my teacher showed me this proof and unfortunately it is vacation now. I don't understand what just happened in the marked line. Can someone please explain?

 

[pasmith]

The line asserts that $$\int_0^\infty e^{-x(1+ y)}x^{m+n-1}\,dx = \frac{\Gamma(m + n)}{(1 + y)^{m + n}}.$$ How would you apply the given formulae to arrive at that?