Question

Solve the following equations.
$\frac{1}{1-\sqrt{1-x}}-\frac{1}{1+\sqrt{1-x}}=\frac{\sqrt{3}}{x}.$

Answer 1

$\frac{1}{1-\sqrt{1-x}}-\frac{1}{1+\sqrt{1-x}}=\frac{\sqrt{3}}{x}$

$\frac{1+\sqrt{1-x}-1+\sqrt{1-x}}{1-(1-x)}=\frac{\sqrt{3}}{x}$

$\frac{2\sqrt{1-x}}{x}=\frac{\sqrt{3}}{x}$

$x\ne 0$

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

Squaring both sides

$4(1-x)=3$

$4-4x=3$

$4x=1$

$x=\frac{1}{4}$