Answer
$\dfrac{1}{x-1}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, the given expression, $
\dfrac{2x}{2x^2-2x}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2x}{2x(x-1)}
\\\\=
\dfrac{\cancel{2x}}{\cancel{2x}(x-1)}
\\\\=
\dfrac{1}{x-1}
.\end{array}
