Answer
$\frac{\sqrt{7}-1}{6}$
Work Step by Step
The given expression is
$=\frac{1}{\sqrt{7}+1}$
The conjugate of $\sqrt{7}+1$ is $\sqrt{7}-1$
$=\frac{1}{\sqrt{7}+1} \cdot \frac{\sqrt{7}-1}{\sqrt{7}-1}$
Use sum and difference pattern.
$=\frac{\sqrt{7}-1}{(\sqrt{7})^2-1^2}$
Simplify.
$=\frac{\sqrt{7}-1}{7-1}$
$=\frac{\sqrt{7}-1}{6}$
