Answer
$\displaystyle \frac{3(3-\sqrt{7})}{2}$
Work Step by Step
Use $(a+b)(a-b)=a^{2}-b^{2}\quad$ when rationalizing.
$[(a+\sqrt{b})(a-\sqrt{b})=a^{2}-b]$
$\displaystyle \frac{3}{3+\sqrt{7}}\cdot\frac{3-\sqrt{7}}{3-\sqrt{7}}=\frac{3(3-\sqrt{7})}{9-7}=\frac{3(3-\sqrt{7})}{2}$
