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\frac{3\times 8}{4\left(1\times 8+7\right)}
Divide \frac{3}{4} by \frac{1\times 8+7}{8} by multiplying \frac{3}{4} by the reciprocal of \frac{1\times 8+7}{8}.
\frac{2\times 3}{7+8}
Cancel out 4 in both numerator and denominator.
\frac{6}{7+8}
Multiply 2 and 3 to get 6.
\frac{6}{15}
Add 7 and 8 to get 15.
\frac{2}{5}
Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.