Question

Solve the following equation:
$\sqrt{x}-\frac{4}{\sqrt{2+x}}+\sqrt{2+x}=0$

Answer 1

$\sqrt{x}-\frac{4}{\sqrt{2+x}}-\sqrt{2+x}=0\sqrt{x}=\frac{4}{\sqrt{2+x}}-\sqrt{2+x}\sqrt{x}=\frac{4-2-x}{\sqrt{2-x}}$

Squaring on both sides

$x=\frac{{(2-x)}^2}{2+x}{x}^2+2x=x^2-4x+46x=4x=\frac{2}{3}$