Answer
$\dfrac{5+\sqrt{21}}{2}$
Work Step by Step
Simplify. $\dfrac{\sqrt 7+\sqrt 3}{\sqrt 7-\sqrt 3}$
Now, $\dfrac{\sqrt 7+\sqrt 3}{\sqrt 7-\sqrt 3}=\dfrac{(\sqrt 7+\sqrt 3)(\sqrt 7 +\sqrt 3)}{(\sqrt 7-\sqrt 3)(\sqrt 7 +\sqrt 3)}$
or, $=\dfrac{(\sqrt7+\sqrt 3)^2}{(\sqrt 7)^2-(\sqrt 3)^2}$
or, $=\dfrac{7+3+2\sqrt{21}}{7-3}$
or, $=\dfrac{5+\sqrt{21}}{2}$
