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\frac{\frac{8}{15}}{\frac{5}{32}\left(\frac{27}{30}+\frac{5}{30}\right)}
Least common multiple of 10 and 6 is 30. Convert \frac{9}{10} and \frac{1}{6} to fractions with denominator 30.
\frac{\frac{8}{15}}{\frac{5}{32}\times \frac{27+5}{30}}
Since \frac{27}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.
\frac{\frac{8}{15}}{\frac{5}{32}\times \frac{32}{30}}
Add 27 and 5 to get 32.
\frac{\frac{8}{15}}{\frac{5}{32}\times \frac{16}{15}}
Reduce the fraction \frac{32}{30} to lowest terms by extracting and canceling out 2.
\frac{\frac{8}{15}}{\frac{5\times 16}{32\times 15}}
Multiply \frac{5}{32} times \frac{16}{15} by multiplying numerator times numerator and denominator times denominator.
\frac{\frac{8}{15}}{\frac{80}{480}}
Do the multiplications in the fraction \frac{5\times 16}{32\times 15}.
\frac{\frac{8}{15}}{\frac{1}{6}}
Reduce the fraction \frac{80}{480} to lowest terms by extracting and canceling out 80.
\frac{8}{15}\times 6
Divide \frac{8}{15} by \frac{1}{6} by multiplying \frac{8}{15} by the reciprocal of \frac{1}{6}.
\frac{8\times 6}{15}
Express \frac{8}{15}\times 6 as a single fraction.
\frac{48}{15}
Multiply 8 and 6 to get 48.
\frac{16}{5}
Reduce the fraction \frac{48}{15} to lowest terms by extracting and canceling out 3.