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\frac{38}{6}+\frac{3}{6}
Least common multiple of 3 and 2 is 6. Convert \frac{19}{3} and \frac{1}{2} to fractions with denominator 6.
\frac{38+3}{6}
Since \frac{38}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.
\frac{41}{6}
Add 38 and 3 to get 41.