Answer
$x=\left\{ -1,\dfrac{1}{2} \right\}$
Work Step by Step
The expression $
\dfrac{2x}{2x-1}+\dfrac{1}{x}=\dfrac{1}{2x-1}
$ simplifies to
\begin{array}{l}
x(2x-1)\left( \dfrac{2x}{2x-1}+\dfrac{1}{x} \right)=\left(\dfrac{1}{2x-1}\right)x(2x-1)
\\\\
x(2x)+1(2x-1)=1(x)
\\\\
2x^2+2x-1=x
\\\\
2x^2+x-1=0
\\\\
(2x-1)(x+1)=0
\\\\
x=\left\{ -1,\dfrac{1}{2} \right\}
.\end{array}
