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