$$u-\frac{u}{a}=t$$
$\left\{\begin{matrix}a=-\frac{u}{t-u}\text{, }&u\neq 0\text{ and }u\neq t\\a\neq 0\text{, }&u=0\text{ and }t=0\end{matrix}\right.$
$t=\frac{u\left(a-1\right)}{a}$
$a\neq 0$
