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