Answer
$x+3y$
Work Step by Step
The given expression, $
\dfrac{\dfrac{x^2-9y^2}{xy}}{\dfrac{1}{y}-\dfrac{3}{x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{x^2-9y^2}{xy}}{\dfrac{x(1)-y(3)}{xy}}
\\\\=
\dfrac{\dfrac{x^2-9y^2}{xy}}{\dfrac{x-3y}{xy}}
\\\\=
\dfrac{x^2-9y^2}{xy}\div\dfrac{x-3y}{xy}
\\\\=
\dfrac{x^2-9y^2}{xy}\cdot\dfrac{xy}{x-3y}
\\\\=
\dfrac{(x+3y)(x-3y)}{xy}\cdot\dfrac{xy}{x-3y}
\\\\=
\dfrac{(x+3y)(\cancel{x-3y})}{\cancel{xy}}\cdot\dfrac{\cancel{xy}}{\cancel{x-3y}}
\\\\=
x+3y
.\end{array}
