Answer
$\frac{2(\sqrt{7}-\sqrt{2})}{5}$
Work Step by Step
We simplify the fraction by multiplying through by $\sqrt{2}-\sqrt{7}$ and using the fact that $(a-b)(a+b)=a^2-b^2$:
$\displaystyle \frac{2}{\sqrt{2}+\sqrt{7}}=\frac{2}{\sqrt{2}+\sqrt{7}} \displaystyle \frac{\sqrt{2}-\sqrt{7}}{\sqrt{2}-\sqrt{7}}=\frac{2(\sqrt{2}-\sqrt{7})}{2-7}=\frac{2(\sqrt{2}-\sqrt{7})}{-5}=\frac{2(\sqrt{7}-\sqrt{2})}{5}$
