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\frac{35}{15}+\frac{12}{15}
Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{4}{5} to fractions with denominator 15.
\frac{35+12}{15}
Since \frac{35}{15} and \frac{12}{15} have the same denominator, add them by adding their numerators.
\frac{47}{15}
Add 35 and 12 to get 47.