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\frac{\left(1\times 2+1\right)\times 5}{2\left(3\times 5+4\right)}
Divide \frac{1\times 2+1}{2} by \frac{3\times 5+4}{5} by multiplying \frac{1\times 2+1}{2} by the reciprocal of \frac{3\times 5+4}{5}.
\frac{\left(2+1\right)\times 5}{2\left(3\times 5+4\right)}
Multiply 1 and 2 to get 2.
\frac{3\times 5}{2\left(3\times 5+4\right)}
Add 2 and 1 to get 3.
\frac{15}{2\left(3\times 5+4\right)}
Multiply 3 and 5 to get 15.
\frac{15}{2\left(15+4\right)}
Multiply 3 and 5 to get 15.
\frac{15}{2\times 19}
Add 15 and 4 to get 19.
\frac{15}{38}
Multiply 2 and 19 to get 38.