Answer
$\dfrac{3xy(y+x)}{(2y+3x)(2y-3x)}$
Work Step by Step
The given expression, $
\dfrac{3x^{-1}+3y^{-1}}{4x^{-2}-9y^{-2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{3}{x}+\dfrac{3}{y}}{\dfrac{4}{x^2}-\dfrac{9}{y^2}}
\\\\=
\dfrac{\dfrac{3y+3x}{xy}}{\dfrac{4y^2-9x^2}{x^2y^2}}
\\\\=
\dfrac{3y+3x}{xy}\div\dfrac{4y^2-9x^2}{x^2y^2}
\\\\=
\dfrac{3y+3x}{xy}\cdot\dfrac{x^2y^2}{4y^2-9x^2}
\\\\=
\dfrac{3(y+x)}{xy}\cdot\dfrac{xy\cdot xy}{(2y+3x)(2y-3x)}
\\\\=
\dfrac{3(y+x)}{\cancel{xy}}\cdot\dfrac{xy\cdot \cancel{xy}}{(2y+3x)(2y-3x)}
\\\\=
\dfrac{3xy(y+x)}{(2y+3x)(2y-3x)}
.\end{array}
