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