Question

Solve the following inequality:
$\frac{x^2-5x+6}{|x|+7}<0$

Answer 1

$x\ge 0$

$\frac{x^2-5x+6}{x+7}<0$

$\frac{(x-2)(x-3)}{x+7}<0$

$x\in (-\infty ,-7)$

and

$x<0$

$\frac{x^2-5x+6}{-x+7}<0$

$\frac{(x-2)(x-3)}{x-7}>0$

$x\in (2,3)\cup (7,\infty )$

$x\in (-\infty ,-7)\cup (2,3)\cup (7,\infty )$