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\frac{\left(1\times 9+1\right)\times 7}{9\left(2\times 7+1\right)}
Divide \frac{1\times 9+1}{9} by \frac{2\times 7+1}{7} by multiplying \frac{1\times 9+1}{9} by the reciprocal of \frac{2\times 7+1}{7}.
\frac{\left(9+1\right)\times 7}{9\left(2\times 7+1\right)}
Multiply 1 and 9 to get 9.
\frac{10\times 7}{9\left(2\times 7+1\right)}
Add 9 and 1 to get 10.
\frac{70}{9\left(2\times 7+1\right)}
Multiply 10 and 7 to get 70.
\frac{70}{9\left(14+1\right)}
Multiply 2 and 7 to get 14.
\frac{70}{9\times 15}
Add 14 and 1 to get 15.
\frac{70}{135}
Multiply 9 and 15 to get 135.
\frac{14}{27}
Reduce the fraction \frac{70}{135} to lowest terms by extracting and canceling out 5.