Answer
$\dfrac{5x}{8}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{3}{x-4}-\dfrac{2}{4-x}}{\dfrac{2}{x-4}-\dfrac{2}{x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{3}{x-4}-\dfrac{2}{-(x-4)}}{\dfrac{2}{x-4}-\dfrac{2}{x}}
\\\\=
\dfrac{\dfrac{3}{x-4}+\dfrac{2}{x-4}}{\dfrac{2}{x-4}-\dfrac{2}{x}}
\\\\=
\dfrac{\dfrac{3+2}{x-4}}{\dfrac{x(2)-(x-4)(2)}{x(x-4)}}
\\\\=
\dfrac{\dfrac{5}{x-4}}{\dfrac{2x-2x+8}{x(x-4)}}
\\\\=
\dfrac{\dfrac{5}{x-4}}{\dfrac{8}{x(x-4)}}
\\\\=
\dfrac{5}{x-4}\div\dfrac{8}{x(x-4)}
\\\\=
\dfrac{5}{x-4}\cdot\dfrac{x(x-4)}{8}
\\\\=
\dfrac{5}{\cancel{x-4}}\cdot\dfrac{x(\cancel{x-4})}{8}
\\\\=
\dfrac{5x}{8}
.\end{array}
