Question

Solve the following inequality:
$\frac{x+1}{x-1}⩾\frac{x+5}{x+1}$

Answer 1

$\frac{x+1}{x-1}\ge \frac{x+5}{x+1}\frac{x+1}{x-1}-\frac{x+5}{x+1}\ge 0\frac{{(x+1)}^2-(x^2+4x-5)}{x^2-1}\ge 0\frac{-2x+6}{x^2-1}\ge 0\frac{x-3}{(x-1)(x+1)}\le 0x\in (-\infty ,-1)\cup (1,3]$