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\frac{45}{6}+\frac{8}{6}
Least common multiple of 2 and 3 is 6. Convert \frac{15}{2} and \frac{4}{3} to fractions with denominator 6.
\frac{45+8}{6}
Since \frac{45}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.
\frac{53}{6}
Add 45 and 8 to get 53.