Rationalising the denominator: $\frac{11}{3\sqrt{3}+7}$ For my homework, I have been asked to rationalise and simplify this surd;

$$\frac{11}{3\sqrt{3}+7}$$

Each time I do this I get the wrong answer. The method I am using is;

$$ \frac{11}{3\sqrt3+7} \times \frac{3\sqrt3-7}{3\sqrt3-7} $$

I ended up with $$\frac{33+11\sqrt3-77}{9+3+21+7\sqrt3-21-7\sqrt3}$$

This ends up no where near the right answer, even once it is simplified. Can someone tell me where I'm going wrong? 

Many thanks!
You're mistakenly multiplying $\rm\; a * b\sqrt{3} \ =\ ab + a\sqrt{3}\:\,\;$ but $\rm\; ab\:\sqrt{3}\;$ is correct.  

In other words $\rm\; b\:\sqrt{3}\;$ means $\rm b * \sqrt{3}\:,\;$ not $\rm\; b + \sqrt{3}\:.$

Also, to rationalize the denominator use $\rm\; (a+b\sqrt 3)\:(a-b\sqrt 3)\ =\ a^2 - 3 b^2$
the answer is

$$-\frac{33\sqrt3-77}{22}$$