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\frac{7}{105}+\frac{3}{105}
Least common multiple of 15 and 35 is 105. Convert \frac{1}{15} and \frac{1}{35} to fractions with denominator 105.
\frac{7+3}{105}
Since \frac{7}{105} and \frac{3}{105} have the same denominator, add them by adding their numerators.
\frac{10}{105}
Add 7 and 3 to get 10.
\frac{2}{21}
Reduce the fraction \frac{10}{105} to lowest terms by extracting and canceling out 5.