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\frac{x^{2}-3x+2}{x-2}
Since \frac{x^{2}-3x}{x-2} and \frac{2}{x-2} have the same denominator, add them by adding their numerators.
\frac{\left(x-2\right)\left(x-1\right)}{x-2}
Factor the expressions that are not already factored in \frac{x^{2}-3x+2}{x-2}.
x-1
Cancel out x-2 in both numerator and denominator.
\frac{x^{2}-3x+2}{x-2}
Since \frac{x^{2}-3x}{x-2} and \frac{2}{x-2} have the same denominator, add them by adding their numerators.
\frac{\left(x-2\right)\left(x-1\right)}{x-2}
Factor the expressions that are not already factored in \frac{x^{2}-3x+2}{x-2}.
x-1
Cancel out x-2 in both numerator and denominator.