Taking Radicals Out of Denominator How does one take radicals out of the denominator of
$$\frac{1}{a + b(\sqrt{2} + \sqrt{3})}$$
assuming $a,b \in \mathbb{Q}$ not both equal to $0$.  I know the trick is to multiply this expression by $1$ s.t. the radicals are removed, but I can't think of such $c/d = 1$ to try.

Try
$$ \frac{ a + b \sqrt{2} - b \sqrt{3} } { a + b \sqrt{2} - b \sqrt{3} } \times \frac{ a - b \sqrt{2} + b \sqrt{3} } { a - b \sqrt{2} + b \sqrt{3} } \times \frac{ a - b \sqrt{2} - b \sqrt{3} } { a - b \sqrt{2} - b \sqrt{3} } .$$
The idea is that you have to multiply by all possible conjugates.
