Answer
$\dfrac{x-9}{x-3\sqrt{x}}$
Work Step by Step
Multiplying by the conjugate of the numerator, then the rationalized-numerator form of the given expression, $ \dfrac{\sqrt{x}+3}{\sqrt{x}} ,$ is \begin{array}{l}\require{cancel} \dfrac{\sqrt{x}+3}{\sqrt{x}}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}-3} \\\\= \dfrac{(\sqrt{x})^2-(3)^2}{\sqrt{x}(\sqrt{x})+\sqrt{x}(-3)} \\\\=
\dfrac{x-9}{x-3\sqrt{x}}
.\end{array}