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\frac{10}{6}-\frac{9}{6}
Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{3}{2} to fractions with denominator 6.
\frac{10-9}{6}
Since \frac{10}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{6}
Subtract 9 from 10 to get 1.