Question

,
$\frac{ |x + 2| }{x - 2} > 0$
​

Answer 1

$\dfrac{|x+2|}{x-2}>0\qquad(x\not =2)\\\\\\1.\ x\in(-\infty,-2\rangle\\\dfrac{-x-2}{x-2}>0\\\\(-x-2)(x-2)>0\\-(x+2)(x-2)>0\\x\in(-2,2)\\\\x\in(-2,2) \wedge x\in(-\infty,-2\rangle\\\underline{x\in\emptyset}\\\\2.\ x\in(-2,2)\cup(2,\infty)\\\dfrac{x+2}{x-2}>0\\\\(x+2)(x-2)>0\\x\in(-\infty-2)\cup(2,\infty)\\\\x\in(-\infty-2)\cup(2,\infty) \wedge x\in(-2,2)\cup(2,\infty)\\\underline{x\in(2,\infty)}\\\\\\x\in\emptyset \vee x\in(2,\infty)\\\boxed{x\in(2,\infty)}$