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\frac{\frac{15}{20}+\frac{8}{20}}{\frac{3}{5}-\frac{1}{2}}
Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{2}{5} to fractions with denominator 20.
\frac{\frac{15+8}{20}}{\frac{3}{5}-\frac{1}{2}}
Since \frac{15}{20} and \frac{8}{20} have the same denominator, add them by adding their numerators.
\frac{\frac{23}{20}}{\frac{3}{5}-\frac{1}{2}}
Add 15 and 8 to get 23.
\frac{\frac{23}{20}}{\frac{6}{10}-\frac{5}{10}}
Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.
\frac{\frac{23}{20}}{\frac{6-5}{10}}
Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{23}{20}}{\frac{1}{10}}
Subtract 5 from 6 to get 1.
\frac{23}{20}\times 10
Divide \frac{23}{20} by \frac{1}{10} by multiplying \frac{23}{20} by the reciprocal of \frac{1}{10}.
\frac{23\times 10}{20}
Express \frac{23}{20}\times 10 as a single fraction.
\frac{230}{20}
Multiply 23 and 10 to get 230.
\frac{23}{2}
Reduce the fraction \frac{230}{20} to lowest terms by extracting and canceling out 10.