Answer
$\dfrac{-7\sqrt[]{11}}{5x}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt[]{99}}{5x}-\sqrt[]{\dfrac{44}{x^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{9\cdot11}}{5x}-\sqrt[]{\dfrac{4}{x^2}\cdot11}
\\\\=
\dfrac{\sqrt[]{(3)^2\cdot11}}{5x}-\sqrt[]{\left( \dfrac{2}{x}\right)^2\cdot11}
\\\\=
\dfrac{3\sqrt[]{11}}{5x}-\dfrac{2\sqrt[]{11}}{x}
\\\\=
\dfrac{3\sqrt[]{11}-5(2\sqrt[]{11})}{5x}
\\\\=
\dfrac{3\sqrt[]{11}-10\sqrt[]{11}}{5x}
\\\\=
\dfrac{-7\sqrt[]{11}}{5x}
.\end{array}
Note that variables are assumed to have positive values.