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\frac{25}{30}+\frac{9}{30}
Least common multiple of 6 and 10 is 30. Convert \frac{5}{6} and \frac{3}{10} to fractions with denominator 30.
\frac{25+9}{30}
Since \frac{25}{30} and \frac{9}{30} have the same denominator, add them by adding their numerators.
\frac{34}{30}
Add 25 and 9 to get 34.
\frac{17}{15}
Reduce the fraction \frac{34}{30} to lowest terms by extracting and canceling out 2.