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Simplify and rationalize the denominator: $$\frac{1}{1+ \frac{1}{\sqrt{2}+1}}.$$

 Feb 21, 2021
 #1
avatar+944 
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\(\frac{1}{\frac{\sqrt{2}+2}{\sqrt{2}+1}} = \frac{\sqrt{2}+1}{\sqrt{2}+2} \cdot \frac{\sqrt{2}-2}{\sqrt{2}-2}\)

 

\(\frac{2 + \sqrt{2} - 2\sqrt{2} - 2}{-2}\)

 

\(\boxed{-\sqrt{2}/2}\)

.
 Feb 21, 2021

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