Question

Solve for $x$:
$\frac{1}{4x}+\frac{1}{6x}=\frac{1}{2x}+\frac{3}{4}$

Answer 1

$\frac{1}{4x}+\frac{1}{6x}=\frac{1}{2x}+\frac{3}{4}$

$\Rightarrow \frac{1}{x}\left(\frac{10}{24}\right)=\frac{4+6x}{8x}$ $\{x\ne 0\}$

$\Rightarrow \frac{5}{12}=\frac{3x+2}{4}$

$\Rightarrow 5=3(3x+2)$

$\Rightarrow 5=9x+6$

$\Rightarrow x=\frac{-1}{9}$.