I am having difficulties solving the following system :
$u \neq t$ and $(t, u) \in \mathbf{R} - \{-1, 1\}$
$\frac{t}{t^2-1}-\frac{u}{u^2-1}=0$
$\:\frac{t^2}{t-1}-\frac{u^2}{u-1}=0$
I tried expanding everything, but I still can't achieve anything
$\frac{tu^2-t-ut^2+u}{\left(t^2-1\right)\left(u^2-1\right)}$
$\frac{t^2u-t^2-u^2t+u^2}{\left(t-1\right)\left(u-1\right)}$
also tried the hint below, ending up finding one equation with the two variables $t(t+1) = u(u+1)$ ... and $u \neq t$
Any idea ?