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\frac{\left(2\times 4+1\right)\times 2}{4\left(1\times 2+1\right)}
Divide \frac{2\times 4+1}{4} by \frac{1\times 2+1}{2} by multiplying \frac{2\times 4+1}{4} by the reciprocal of \frac{1\times 2+1}{2}.
\frac{1+2\times 4}{2\left(1+2\right)}
Cancel out 2 in both numerator and denominator.
\frac{1+8}{2\left(1+2\right)}
Multiply 2 and 4 to get 8.
\frac{9}{2\left(1+2\right)}
Add 1 and 8 to get 9.
\frac{9}{2\times 3}
Add 1 and 2 to get 3.
\frac{9}{6}
Multiply 2 and 3 to get 6.
\frac{3}{2}
Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.