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\frac{\left(a-4\right)\left(a-5\right)}{\left(a-4\right)\left(a-2\right)}
Divide \frac{a-4}{\left(a-4\right)\left(a-2\right)} by \frac{1}{a-5} by multiplying \frac{a-4}{\left(a-4\right)\left(a-2\right)} by the reciprocal of \frac{1}{a-5}.
\frac{a-5}{a-2}
Cancel out a-4 in both numerator and denominator.
\frac{\left(a-4\right)\left(a-5\right)}{\left(a-4\right)\left(a-2\right)}
Divide \frac{a-4}{\left(a-4\right)\left(a-2\right)} by \frac{1}{a-5} by multiplying \frac{a-4}{\left(a-4\right)\left(a-2\right)} by the reciprocal of \frac{1}{a-5}.
\frac{a-5}{a-2}
Cancel out a-4 in both numerator and denominator.