rationalize

$\frac{1}{\frac{\sqrt{2}+2}{\sqrt{2}+1}} = \frac{\sqrt{2}+1}{\sqrt{2}+2} \cdot \frac{\sqrt{2}-2}{\sqrt{2}-2}$

$\frac{2 + \sqrt{2} - 2\sqrt{2} - 2}{-2}$

$\boxed{-\sqrt{2}/2}$