Answer
$\dfrac{x}{5(x-2)}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{4}{5-x}+\dfrac{5}{x-5}}{\dfrac{2}{x}+\dfrac{3}{x-5}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{4}{-(x-5)}+\dfrac{5}{x-5}}{\dfrac{(x-5)(2)+x(3)}{x(x-5)}}
\\\\=
\dfrac{\dfrac{-4+5}{x-5}}{\dfrac{2x-10+3x}{x(x-5)}}
\\\\=
\dfrac{\dfrac{1}{x-5}}{\dfrac{5x-10}{x(x-5)}}
\\\\=
\dfrac{\dfrac{1}{x-5}}{\dfrac{5(x-2)}{x(x-5)}}
\\\\=
\dfrac{1}{x-5}\div\dfrac{5(x-2)}{x(x-5)}
\\\\=
\dfrac{1}{x-5}\cdot\dfrac{x(x-5)}{5(x-2)}
\\\\=
\dfrac{1}{\cancel{x-5}}\cdot\dfrac{x(\cancel{x-5})}{5(x-2)}
\\\\=
\dfrac{x}{5(x-2)}
.\end{array}
