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\frac{8}{6}-\frac{15}{6}
Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{5}{2} to fractions with denominator 6.
\frac{8-15}{6}
Since \frac{8}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.
-\frac{7}{6}
Subtract 15 from 8 to get -7.