Question

Solve the following equations and verify your answer :

$\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$

Answer 1

$\frac{2}{3x}-\frac{3}{2x}=\frac{1}{12}$
(By cross multiplication)
$\frac{4-9}{6x}=\frac{1}{12}\Rightarrow \frac{-5}{6x}=\frac{1}{12}\Rightarrow 6x=-5\times 12\Rightarrow x=\frac{-5\times 12}{6}=-10\therefore x=-10$
Verification :
$L.H.S.=\frac{2}{3x}-\frac{3}{2x}=\frac{2}{3(-10)}-\frac{3}{2(-10)}=\frac{2}{-30}-\frac{3}{-20}=\frac{1}{-15}+\frac{3}{20}=\frac{-4+9}{60}=\frac{5}{60}=\frac{1}{12}=R.H.S.$