Answer
$\displaystyle6+2\sqrt{2}$
Work Step by Step
We multiply the numerator and denominator by $3+\sqrt{2}$ and use the fact that $(a-b)(a+b)=a^2-b^2$ to simplify:
$\displaystyle \frac{14}{3-\sqrt{2}}=\frac{14}{3-\sqrt{2}}\cdot\frac{3+\sqrt{2}}{3+\sqrt{2}}=\frac{42+14\sqrt{2}}{3^{2}-(\sqrt{2})^{2}}=\frac{42+14\sqrt{2}}{9-2}=\frac{42+14\sqrt{2}}{7}=6+2\sqrt{2}$
