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