Question

Solve the following equation:
$\frac{x-4}{\sqrt{x}+2}=x-8$

Answer 1

$\frac{x-4}{\sqrt{x}+2}=x-8(\sqrt{x}\ne -2)$

$⟹\frac{(\sqrt{x}{)}^2-(2{)}^2}{\sqrt{x}+2}=x-8$

$\sqrt{x}-2=x-8⟹x-\sqrt{x}-6=0⟹\sqrt{x}=-2,3$ (As $\sqrt{x}$ cannot be negative)

$\sqrt{x}=3⟹x=9$