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\frac{4}{24}+\frac{15}{24}
Least common multiple of 6 and 8 is 24. Convert \frac{1}{6} and \frac{5}{8} to fractions with denominator 24.
\frac{4+15}{24}
Since \frac{4}{24} and \frac{15}{24} have the same denominator, add them by adding their numerators.
\frac{19}{24}
Add 4 and 15 to get 19.