Question

Solve the following inequality:
$\frac{4}{1+x}+\frac{2}{1-x}<1$

Answer 1

$\frac{4}{1+x}+\frac{2}{1-x}<1⟹\frac{4-4x+2+2x}{1-x^2}<1⟹\frac{6-2x-1+x^2}{1-x^2}<0⟹\frac{x^2-2x+5}{1-x^2}<0⟹x^2-1>0$

$⟹x\in (-\infty ,-1)\cup (1,\infty )$