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

Nothing went wrong
If you take your result $\dfrac{2-2\sqrt 6 }{-5}$
Multiply num and den by $-1$ and collect $2$ in the numerator, you get
$$\dfrac{2(\sqrt 6 -1)}{5}$$ which is the result of the book
