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\frac{\left(a-b\right)\times 9}{9\times 10\left(a-b\right)}
Divide \frac{a-b}{9} by \frac{10\left(a-b\right)}{9} by multiplying \frac{a-b}{9} by the reciprocal of \frac{10\left(a-b\right)}{9}.
\frac{1}{10}
Cancel out 9\left(a-b\right) in both numerator and denominator.