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-\frac{1}{6}-\frac{2}{6}
Least common multiple of 6 and 3 is 6. Convert -\frac{1}{6} and \frac{1}{3} to fractions with denominator 6.
\frac{-1-2}{6}
Since -\frac{1}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{-3}{6}
Subtract 2 from -1 to get -3.
-\frac{1}{2}
Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.