Question

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

Answer 1

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

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

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

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

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

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

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

$x\in (-\infty ,-1)\cup (0,\frac{1}{2})\cup (1,\infty )$