Answer
$\dfrac{x-3y}{x+3y}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{2}{y^2}-\dfrac{5}{xy}-\dfrac{3}{x^2}}{\dfrac{2}{y^2}+\dfrac{7}{xy}+\dfrac{3}{x^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{x^2(2)-xy(5)-y^2(3)}{x^2y^2}}{\dfrac{x^2(2)+xy(7)+y^2(3)}{x^2y^2}}
\\\\=
\dfrac{\dfrac{x^2(2)-xy(5)-y^2(3)}{\cancel{x^2y^2}}}{\dfrac{x^2(2)+xy(7)+y^2(3)}{\cancel{x^2y^2}}}
\\\\=
\dfrac{x^2(2)-xy(5)-y^2(3)}{x^2(2)+xy(7)+y^2(3)}
\\\\=
\dfrac{2x^2-5xy-3y^2}{2x^2+7xy+3y^2}
\\\\=
\dfrac{(2x+y)(x-3y)}{(2x+y)(x+3y)}
\\\\=
\dfrac{(\cancel{2x+y})(x-3y)}{(\cancel{2x+y})(x+3y)}
\\\\=
\dfrac{x-3y}{x+3y}
.\end{array}
