TeX source:

\begin{aligned}(x+1)(x-1)\left[\dfrac{-4 x}{x-1}+\dfrac{4}{x+1}\right] &=\left[\dfrac{-8}{(x+1)(x-1)}\right](x+1)(x-1) \\-4 x(x+1)+4(x-1) &=-8 \\-4 x^{2}-4 x+4 x-4 &=-8 \\-4 x^{2}+4 &=0 \\-4\left(x^{2}-1\right) &=0 \\-4(x+1)(x-1) &=0 \\ x &=-1 \\ x &=1 \end{aligned}