Answer
$\frac{13-3\sqrt {21}}{5}$
Work Step by Step
$\frac{\sqrt 3-\sqrt 7}{2\sqrt 3+\sqrt 7}\times\frac{2\sqrt 3-\sqrt 7}{2\sqrt 3-\sqrt 7}$
=$\frac{(\sqrt 3-\sqrt 7)(2\sqrt 3-\sqrt 7)}{(2\sqrt 3+\sqrt 7)(2\sqrt 3-\sqrt 7)}$
=$\frac{\sqrt 3(2\sqrt 3-\sqrt 7)-\sqrt 7(2\sqrt 3-\sqrt 7)}{(2\sqrt 3)^{2}-(\sqrt 7)^{2}}$
=$\frac{2(3)-\sqrt 7\sqrt 3-2\sqrt 7\sqrt 3+7}{(2\sqrt 3)^{2}-(\sqrt 7)^{2}}$
=$\frac{6-\sqrt {21}-2\sqrt {21}+7}{4(3)-7}$
=$\frac{6+7+(-1-2)\sqrt {21}}{12-7}$
=$\frac{13-3\sqrt {21}}{5}$
