Rationalising the denominator surds I have been struggling on this question. I don't understand how to change a negative surd fraction to a positive surd fraction.
Question: Rationalise and simply
              $$\frac{2}{1+{\sqrt 6}}$$
What I did:
$\frac{2(1-{\sqrt 6})}{(1+{\sqrt 6)(1-{\sqrt 6})}}$
=  $\frac{2{-2\sqrt 6 }}{-5}$
When I checked the answers It said the answer was 
$$\frac{2({\sqrt 6} -1)}{5}$$
What did I do wrong
Thank you and help is appreciated

$$\frac{2}{\sqrt6+1}$$
$$\frac{2}{\sqrt6+1}\times \frac{\sqrt6-1}{\sqrt6-1}$$
$$\frac{2(\sqrt6-1)}{6-1}$$
$$\frac{2(\sqrt6-1)}{5}$$
Comments
Try with $\sqrt6-1$ instead of $1- \sqrt6$
