Question

Solve the following equation:
$\frac{x}{x+1}-2\sqrt{\frac{x+1}{x}}=3$

Answer 1

put $t^2=\frac{x}{x+1}$

$⟹t^2-\frac{2}{t}-3=0$

$⟹t^3-3t-2=0$

$t=-1,2$

$x=\frac{-4}{3}$