Question

Solve: $\frac{x-2}{x+2}+\frac{x+2}{x-2}=4$

Answer 1

$\frac{x-2}{x+2}+\frac{x+2}{x-2}=4$

$\Rightarrow (x-2{)}^2+(x+2{)}^2=4(x^2-4)$

$\Rightarrow 2(x^2+4)=4x^2-16$

$\Rightarrow 2x^2+8=4x^2-16$

$\Rightarrow 2x^2=24$

$\Rightarrow x^2=12$

$\Rightarrow x=\sqrt{1}2=2\sqrt{3}$