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\frac{1}{\frac{1+1}{2}}
Since \frac{1}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.
\frac{1}{\frac{2}{2}}
Add 1 and 1 to get 2.
\frac{1}{1}
Divide 2 by 2 to get 1.
1
Anything divided by one gives itself.