Answer
$\dfrac{-1}{\sqrt{x-h}+\sqrt{x}}$
Work Step by Step
Multiplying by the conjugate of the numerator, the rationalized-numerator form of the given expression, $
\dfrac{\sqrt{x-h}-\sqrt{x}}{h}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{x-h}-\sqrt{x}}{h}\cdot\dfrac{\sqrt{x-h}+\sqrt{x}}{\sqrt{x-h}+\sqrt{x}}
\\\\=
\dfrac{(\sqrt{x-h})^2-(\sqrt{x})^2}{h(\sqrt{x-h})+h(\sqrt{x})}
\\\\=
\dfrac{x-h-x}{h\sqrt{x-h}+h\sqrt{x}}
\\\\=
\dfrac{-h}{h\sqrt{x-h}+h\sqrt{x}}
\\\\=
\dfrac{-\cancel{h}}{\cancel{h}\sqrt{x-h}+\cancel{h}\sqrt{x}}
\\\\=
\dfrac{-1}{\sqrt{x-h}+\sqrt{x}}
.\end{array}
