$$\frac{1}{x+1}+\frac{2}{1+v^{2}}-\frac{4}{1-v^{4}}$$
$-\frac{2x+v^{2}+1}{\left(x+1\right)\left(1-v^{2}\right)}$
$-\frac{1}{\left(x+1\right)^{2}}$