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