Answer
$\dfrac{x+4}{4}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{x}{4}-\dfrac{4}{x}}{1-\dfrac{4}{x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{x^2-16}{4x}}{\dfrac{x-4}{x}}
\\\\=
\dfrac{x^2-16}{4x}\div\dfrac{x-4}{x}
\\\\=
\dfrac{x^2-16}{4x}\cdot\dfrac{x}{x-4}
\\\\=
\dfrac{(x+4)(x-4)}{4x}\cdot\dfrac{x}{x-4}
\\\\=
\dfrac{(x+4)(\cancel{x-4})}{4\cancel{x}}\cdot\dfrac{\cancel{x}}{\cancel{x-4}}
\\\\=
\dfrac{x+4}{4}
.\end{array}