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\frac{15}{12}-\frac{8}{12}
Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{2}{3} to fractions with denominator 12.
\frac{15-8}{12}
Since \frac{15}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.
\frac{7}{12}
Subtract 8 from 15 to get 7.