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\frac{1}{\sqrt{1+1}}
Divide 4 by 4 to get 1.
\frac{1}{\sqrt{2}}
Add 1 and 1 to get 2.
\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}
Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.
\frac{\sqrt{2}}{2}
The square of \sqrt{2} is 2.