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