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