Answer
$x=-2$
Work Step by Step
Given : $\frac{x+4}{2x} = \frac{2}{2x}$
This becomes : $x+4=2$
(After multiplying both the sides by $2x$)
Thus, $x=2-4=-2$
Checking by putting the value $x=-2$ in the original equation :
Left Hand Side, $LHS = \frac{-2+4}{2\times-2}=\frac{-2}{4}=\frac{-1}{2}$
Right Hand Side, $RHS=\frac{2}{2\times-2}=\frac{-1}{2}$
Thus, $LHS=RHS$
