Question

Solve the following inequality:
$\frac{x^2-2x+2^{|a|}}{x^2-a^2}>0$

Answer 1

$x^2-2x+2^{|a|}=(x-1{)}^2+(2^{|a|}-1)\ge 0$

$\frac{x^2-2x+2^{|a|}}{x^2-a^2}>0$

$⟹x^2-a^2>0⟹x\in (-\infty ,-a)\cup (a,\infty )$