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\frac{21}{6}+\frac{4}{6}+\frac{5}{6}
Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{2}{3} to fractions with denominator 6.
\frac{21+4}{6}+\frac{5}{6}
Since \frac{21}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.
\frac{25}{6}+\frac{5}{6}
Add 21 and 4 to get 25.
\frac{25+5}{6}
Since \frac{25}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.
\frac{30}{6}
Add 25 and 5 to get 30.
5
Divide 30 by 6 to get 5.