Question

Solve : $\frac{x}{a}-\frac{a+b}{x}=\frac{b(a+b)}{ax}$.

Answer 1

Taking LCM

$\frac{x^2-a(a+b)}{ax}$=$\frac{b(a+b)}{ax}$

$x^2-a^2-ab$=$ab+b^2$

$x^2-a^2-2ab-b^2=0$

$x^2-{(a+b)}^2=0$
$x^2={(a+b)}^2$

Taking square root on both side
$x=\pm (a+b)$