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\frac{\left(x^{2}-4x+3\right)\left(x-2\right)}{\left(x^{2}-3x+2\right)\left(x-3\right)}
Divide \frac{x^{2}-4x+3}{x^{2}-3x+2} by \frac{x-3}{x-2} by multiplying \frac{x^{2}-4x+3}{x^{2}-3x+2} by the reciprocal of \frac{x-3}{x-2}.
\frac{\left(x-3\right)\left(x-2\right)\left(x-1\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}
Factor the expressions that are not already factored.
1
Cancel out \left(x-3\right)\left(x-2\right)\left(x-1\right) in both numerator and denominator.