Answer
$\frac{-7+2\sqrt {14}+\sqrt 7-2\sqrt 2}{2}$
Work Step by Step
Multiply $\frac{2\sqrt 7-4\sqrt 2}{2\sqrt 7-4\sqrt 2}$ to the expression, we have:
$\frac{\sqrt 7-1}{2\sqrt 7+4\sqrt 2}\cdot \frac{2\sqrt 7-4\sqrt 2}{2\sqrt 7-4\sqrt 2}=\frac{14-4\sqrt {14}-2\sqrt 7+4\sqrt 2}{28-32}=\frac{14-4\sqrt {14}-2\sqrt 7+4\sqrt 2}{-4}=\frac{-7+2\sqrt {14}+\sqrt 7-2\sqrt 2}{2}$
