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\frac{\frac{8}{20}+\frac{15}{20}-\frac{1}{6}}{\frac{2}{3}}
Least common multiple of 5 and 4 is 20. Convert \frac{2}{5} and \frac{3}{4} to fractions with denominator 20.
\frac{\frac{8+15}{20}-\frac{1}{6}}{\frac{2}{3}}
Since \frac{8}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.
\frac{\frac{23}{20}-\frac{1}{6}}{\frac{2}{3}}
Add 8 and 15 to get 23.
\frac{\frac{69}{60}-\frac{10}{60}}{\frac{2}{3}}
Least common multiple of 20 and 6 is 60. Convert \frac{23}{20} and \frac{1}{6} to fractions with denominator 60.
\frac{\frac{69-10}{60}}{\frac{2}{3}}
Since \frac{69}{60} and \frac{10}{60} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{59}{60}}{\frac{2}{3}}
Subtract 10 from 69 to get 59.
\frac{59}{60}\times \frac{3}{2}
Divide \frac{59}{60} by \frac{2}{3} by multiplying \frac{59}{60} by the reciprocal of \frac{2}{3}.
\frac{59\times 3}{60\times 2}
Multiply \frac{59}{60} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{177}{120}
Do the multiplications in the fraction \frac{59\times 3}{60\times 2}.
\frac{59}{40}
Reduce the fraction \frac{177}{120} to lowest terms by extracting and canceling out 3.