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\frac{\frac{5}{10}+\frac{4}{10}}{1-\frac{1}{10}}
Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.
\frac{\frac{5+4}{10}}{1-\frac{1}{10}}
Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.
\frac{\frac{9}{10}}{1-\frac{1}{10}}
Add 5 and 4 to get 9.
\frac{\frac{9}{10}}{\frac{10}{10}-\frac{1}{10}}
Convert 1 to fraction \frac{10}{10}.
\frac{\frac{9}{10}}{\frac{10-1}{10}}
Since \frac{10}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{9}{10}}{\frac{9}{10}}
Subtract 1 from 10 to get 9.
1
Divide \frac{9}{10} by \frac{9}{10} to get 1.