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\frac{2}{30}+\frac{51}{30}
Least common multiple of 15 and 10 is 30. Convert \frac{1}{15} and \frac{17}{10} to fractions with denominator 30.
\frac{2+51}{30}
Since \frac{2}{30} and \frac{51}{30} have the same denominator, add them by adding their numerators.
\frac{53}{30}
Add 2 and 51 to get 53.