Answer
$\dfrac{5x}{2}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{3}{x-1}-\dfrac{2}{1-x}}{\dfrac{2}{x-1}-\dfrac{2}{x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{3}{x-1}-\dfrac{2}{-(x-1)}}{\dfrac{2}{x-1}-\dfrac{2}{x}}
\\\\=
\dfrac{\dfrac{3}{x-1}+\dfrac{2}{x-1}}{\dfrac{2}{x-1}-\dfrac{2}{x}}
\\\\=
\dfrac{\dfrac{3+2}{x-1}}{\dfrac{x(2)-(x-1)(2)}{x(x-1)}}
\\\\=
\dfrac{\dfrac{5}{x-1}}{\dfrac{2x-2x+2}{x(x-1)}}
\\\\=
\dfrac{\dfrac{5}{x-1}}{\dfrac{2}{x(x-1)}}
\\\\=
\dfrac{5}{x-1}\div\dfrac{2}{x(x-1)}
\\\\=
\dfrac{5}{x-1}\cdot\dfrac{x(x-1)}{2}
\\\\=
\dfrac{5}{\cancel{x-1}}\cdot\dfrac{x(\cancel{x-1})}{2}
\\\\=
\dfrac{5x}{2}
.\end{array}