Answer
$3(\sqrt{5}-\sqrt{3})$
Work Step by Step
Use $(a+b)(a-b)=a^{2}-b^{2}\quad$ when rationalizing.
$[(a+\sqrt{b})(a-\sqrt{b})=a^{2}-b]$
$\displaystyle \frac{6}{\sqrt{5}+\sqrt{3}}\cdot\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}=\frac{6(\sqrt{5}-\sqrt{3})}{5-3}=$
$=\displaystyle \frac{6(\sqrt{5}-\sqrt{3})}{2}=3(\sqrt{5}-\sqrt{3})$
