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\frac{4}{6}-\frac{9}{6}
Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{3}{2} to fractions with denominator 6.
\frac{4-9}{6}
Since \frac{4}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.
-\frac{5}{6}
Subtract 9 from 4 to get -5.