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\frac{\left(90-10\right)\times 90}{10\left(10-90\right)}
Divide \frac{90-10}{10} by \frac{10-90}{90} by multiplying \frac{90-10}{10} by the reciprocal of \frac{10-90}{90}.
\frac{-90\left(10-90\right)}{10\left(10-90\right)}
Extract the negative sign in 90-10.
-9
Cancel out 10\left(10-90\right) in both numerator and denominator.