Answer
$-\frac{1}{2\sqrt 7+6}$
Work Step by Step
$\frac{\sqrt 7-3}{4}=\frac{\sqrt 7-3}{4}\frac{\sqrt 7+3}{\sqrt 7+3}=\frac{\sqrt 7\sqrt 7+3\sqrt 7-3\sqrt 7-3\times3}{4\sqrt 7+4\times3}=\frac{(\sqrt 7)^2-9}{4\sqrt 7+12}=\frac{7-9}{4\sqrt 7+12}=\frac{-2}{2(2\sqrt 7+6)}=\frac{-1}{2\sqrt 7+6}=-\frac{1}{2\sqrt 7+6}$
