Answer
$\dfrac{\sqrt{35}-\sqrt{21}}{2}$
Work Step by Step
Simplify. $\dfrac{\sqrt7}{\sqrt5+\sqrt3}$
Now, $\dfrac{\sqrt7}{\sqrt5+\sqrt3}=\dfrac{\sqrt7(\sqrt5-\sqrt3)}{(\sqrt5+\sqrt3)(\sqrt5-\sqrt3)}$
or, $=\dfrac{\sqrt7\sqrt5-\sqrt7\sqrt3)}{(\sqrt5)^2-(\sqrt3)^2}$
or, $=\dfrac{\sqrt{35}-\sqrt{21}}{2}$
