Answer
$\dfrac{x-4}{5\sqrt{x}-10}$
Work Step by Step
Multiplying by the conjugate of the numerator, the rationalized-numerator form of the given expression, $
\dfrac{\sqrt[]{x}+2}{5}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{x}+2}{5}\cdot\dfrac{\sqrt[]{x}-2}{\sqrt[]{x}-2}
\\\\=
\dfrac{(\sqrt[]{x})^2-2^2}{5\sqrt{x}-10}
\\\\=
\dfrac{x-4}{5\sqrt{x}-10}
.\end{array}
