Answer
$\displaystyle \frac{17\sqrt{10}+34}{6}$
Work Step by Step
We lose the square roots in the denominator by applying the difference of squares formula:
$(a\sqrt{x}+b\sqrt{y})(a\sqrt{x}-b\sqrt{y})=(a\sqrt{x})^{2}-(b\sqrt{y})^{2}=a^{2}x-b^{2}y$
$\displaystyle \frac{17}{\sqrt{10}-2} \displaystyle \color{red}{ \cdot\frac{\sqrt{10}+2}{\sqrt{10}+2} }\qquad$ (rationalize)
$ =\displaystyle \frac{17(\sqrt{10}+2)}{(\sqrt{10})^{2}-2^{2}} =\frac{17(\sqrt{10}+2)}{10-4} =\frac{17(\sqrt{10}+2)}{6}$
= $\displaystyle \frac{17\sqrt{10}+34}{6}$
