+1678 Simplify and rationalize the denominator: $$\frac{1}{1+ \frac{1}{\sqrt{2}+1}}.$$
+1223 \(\frac{1}{\frac{\sqrt{2}+2}{\sqrt{2}+1}} = \frac{\sqrt{2}+1}{\sqrt{2}+2} \cdot \frac{\sqrt{2}-2}{\sqrt{2}-2}\)
\(\frac{2 + \sqrt{2} - 2\sqrt{2} - 2}{-2}\)
\(\boxed{-\sqrt{2}/2}\)
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