$$\frac{\partial f}{\partial a}=(\frac{a}{a-1})y-z$$
$\left\{\begin{matrix}a=\frac{z}{z-y}\text{, }&y\neq 0\text{ and }y\neq z\\a\neq 1\text{, }&z=0\text{ and }y=0\end{matrix}\right.$
$f\in \mathrm{R}$
$z=\frac{ay}{a-1}\text{ and }a\neq 1$
