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-\frac{3}{6}-\frac{8}{6}
Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.
\frac{-3-8}{6}
Since -\frac{3}{6} and \frac{8}{6} have the same denominator, subtract them by subtracting their numerators.
-\frac{11}{6}
Subtract 8 from -3 to get -11.