Answer
$\displaystyle \frac{\sqrt{ab}-b}{a-b}$
Work Step by Step
We lose the square roots in the denominator by applying the difference of squares formula:
$(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}=a^{2}x-b^{2}y$
$\displaystyle \frac{\sqrt{b}}{\sqrt{a}-\sqrt{b}} \displaystyle \color{red}{ \cdot\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}} }\qquad$ (rationalize)
$ =\displaystyle \frac{\sqrt{b}(\sqrt{a}+\sqrt{b})}{(\sqrt{a})^{2}-(\sqrt{b})^{2}} =\frac{\sqrt{b}(\sqrt{a}+\sqrt{b})}{a-b} $
$=\displaystyle \frac{\sqrt{b}\cdot\sqrt{a}-(\sqrt{b})^{2}}{a-b}$
= $\displaystyle \frac{\sqrt{ab}-b}{a-b}$
