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