I am not sure if I took down the correct notes but...

In rationalizing denominators, we multiply the denominator on both the top and bottom as such

$\displaystyle \frac{9}{\sqrt{2+7}}$X$\displaystyle \frac{(\sqrt{2-7})}{(\sqrt{2-7})}

$

= $\displaystyle \frac{9(\sqrt{2-7})}{(\sqrt{4-7})(\sqrt{2-7})(\sqrt{2-49})}$

$\displaystyle \frac{9(\sqrt{2-7})}{-47}$in order to get rid of the negative we multiply by (-1) and get$\displaystyle \frac{-9(\sqrt{2-7})}{47}$

again did I write my notes in the wrong way?!

The problem I'm trying to work out is $\displaystyle \frac{\sqrt{6}}{\sqrt{5+9}}$

Thanks