Answer
$\frac{\sqrt{21}-3}{4}$
Work Step by Step
The given expression is
$=\frac{\sqrt{3}}{\sqrt{7}+\sqrt{3}}$
The conjugate of $\sqrt{7}+\sqrt{3}$ is $\sqrt{7}-\sqrt{3}$
$=\frac{\sqrt{3}}{\sqrt{7}+\sqrt{3}} \cdot \frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}-\sqrt{3}}$
Use sum and difference pattern.
$=\frac{\sqrt{3}(\sqrt{7}-\sqrt{3})}{(\sqrt{7})^2-(\sqrt{3})^2}$
Simplify.
$=\frac{\sqrt{3\cdot 7}-\sqrt{3} \cdot \sqrt{3}}{7-3}$
$=\frac{\sqrt{21}-3}{4}$.
