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\frac{24}{38}+\frac{7}{38}
Least common multiple of 19 and 38 is 38. Convert \frac{12}{19} and \frac{7}{38} to fractions with denominator 38.
\frac{24+7}{38}
Since \frac{24}{38} and \frac{7}{38} have the same denominator, add them by adding their numerators.
\frac{31}{38}
Add 24 and 7 to get 31.