Every time I think I understand how to deal with a minus in a question, something different crops up. I thought I could do this but I need a little help on the last stage.

Rewrite the expression with a rational denominator. $\displaystyle \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+4}$

$\displaystyle \frac{(\sqrt{3}+\sqrt{2})(\sqrt{3}-4)}{(\sqrt{3}+4)(\sqrt{3}-4)}$

=$\displaystyle \frac{(\sqrt{3}+\sqrt{2})(\sqrt{3}-4)}{-13}$

Now what do I do to get rid of the minus on the denominator?

I know the answer is $\displaystyle -\frac{(\sqrt{3}+2)(\sqrt{3}-4)}{13}$ but cannot fathom how they got there.

If I multiply top and bottom by -13, don't I end up with $\displaystyle -13(\sqrt{3}+2)(\sqrt{3}-4)$