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