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\frac{\frac{2}{2}-\frac{1}{2}}{1+\frac{1}{2}}
Convert 1 to fraction \frac{2}{2}.
\frac{\frac{2-1}{2}}{1+\frac{1}{2}}
Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{1}{2}}{1+\frac{1}{2}}
Subtract 1 from 2 to get 1.
\frac{\frac{1}{2}}{\frac{2}{2}+\frac{1}{2}}
Convert 1 to fraction \frac{2}{2}.
\frac{\frac{1}{2}}{\frac{2+1}{2}}
Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.
\frac{\frac{1}{2}}{\frac{3}{2}}
Add 2 and 1 to get 3.
\frac{1}{2}\times \frac{2}{3}
Divide \frac{1}{2} by \frac{3}{2} by multiplying \frac{1}{2} by the reciprocal of \frac{3}{2}.
\frac{1\times 2}{2\times 3}
Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{1}{3}
Cancel out 2 in both numerator and denominator.