Gamma variables with a common scale: $X/(X+Y)\sim$ Beta$(\alpha,\beta)$

Suppose X and Y are independent r.v.'s such that $f(x)=\dfrac{e^{-x}x^{\alpha-1}}{\Gamma(\alpha)}$, $x>0$, $\alpha>0$ and $f(y)=\dfrac{e^{-y}y^{\beta-1}}{\Gamma(\beta)}$, $y>0$, $\beta>0$. The distribution of $\dfrac X{X+Y}$ is: