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\frac{20}{24}+\frac{39}{24}
Least common multiple of 6 and 8 is 24. Convert \frac{5}{6} and \frac{13}{8} to fractions with denominator 24.
\frac{20+39}{24}
Since \frac{20}{24} and \frac{39}{24} have the same denominator, add them by adding their numerators.
\frac{59}{24}
Add 20 and 39 to get 59.