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