Answer
$\dfrac{2(2z+1)}{-3z}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{z}{5}+\dfrac{1}{10}}{\dfrac{z}{20}-\dfrac{z}{5}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{2(z)+1(1)}{10}}{\dfrac{1(z)-4(z)}{20}}
\\\\=
\dfrac{\dfrac{2z+1}{10}}{\dfrac{z-4z}{20}}
\\\\=
\dfrac{\dfrac{2z+1}{10}}{\dfrac{-3z}{20}}
\\\\=
\dfrac{2z+1}{10}\div\dfrac{-3z}{20}
\\\\=
\dfrac{2z+1}{10}\cdot\dfrac{20}{-3z}
\\\\=
\dfrac{2z+1}{\cancel{10}}\cdot\dfrac{\cancel{10}\cdot2}{-3z}
\\\\=
\dfrac{2(2z+1)}{-3z}
.\end{array}
