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\frac{10}{90}+\frac{9}{90}
Least common multiple of 9 and 10 is 90. Convert \frac{1}{9} and \frac{1}{10} to fractions with denominator 90.
\frac{10+9}{90}
Since \frac{10}{90} and \frac{9}{90} have the same denominator, add them by adding their numerators.
\frac{19}{90}
Add 10 and 9 to get 19.