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\frac{1\left(\frac{3}{6}-\frac{2}{6}\right)\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.
\frac{1\times \frac{3-2}{6}\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{1\times \frac{1}{6}\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Subtract 2 from 3 to get 1.
\frac{\frac{1}{6}\left(2-\frac{1}{5}\right)}{1-\frac{1}{3}}
Multiply 1 and \frac{1}{6} to get \frac{1}{6}.
\frac{\frac{1}{6}\left(\frac{10}{5}-\frac{1}{5}\right)}{1-\frac{1}{3}}
Convert 2 to fraction \frac{10}{5}.
\frac{\frac{1}{6}\times \frac{10-1}{5}}{1-\frac{1}{3}}
Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{1}{6}\times \frac{9}{5}}{1-\frac{1}{3}}
Subtract 1 from 10 to get 9.
\frac{\frac{1\times 9}{6\times 5}}{1-\frac{1}{3}}
Multiply \frac{1}{6} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{9}{30}}{1-\frac{1}{3}}
Do the multiplications in the fraction \frac{1\times 9}{6\times 5}.
\frac{\frac{3}{10}}{1-\frac{1}{3}}
Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.
\frac{\frac{3}{10}}{\frac{3}{3}-\frac{1}{3}}
Convert 1 to fraction \frac{3}{3}.
\frac{\frac{3}{10}}{\frac{3-1}{3}}
Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{3}{10}}{\frac{2}{3}}
Subtract 1 from 3 to get 2.
\frac{3}{10}\times \frac{3}{2}
Divide \frac{3}{10} by \frac{2}{3} by multiplying \frac{3}{10} by the reciprocal of \frac{2}{3}.
\frac{3\times 3}{10\times 2}
Multiply \frac{3}{10} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{9}{20}
Do the multiplications in the fraction \frac{3\times 3}{10\times 2}.