Question

Solve the following equations
$\frac{x-1}{x+1}-\frac{x}{x-2}<0$

Answer 1

$\frac{x-1}{x+1}-\frac{x}{x-2}<0$

$\frac{x+1-2}{x+1}-\frac{x-2+2}{x-2}<0$

$\frac{x+1}{x+1}-\frac{2}{x+1}-\frac{x-2}{x-2}-\frac{2}{x-2}<0$

$1-\frac{2}{x+1}-1-\frac{2}{x-2}<0$

$\frac{2}{x+1}+\frac{2}{x-2}>0$

$\frac{2(x-2+x+1)}{(x+1)(x-2)}>0$

$\frac{2x-2}{(x+1)(x-2)}>0$

$2x-2>0$

$x>1$

$\therefore x\in (1,\infty )-\{-1,2\}$