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\frac{\left(x+y\right)\left(x-y\right)}{x-y}-2x+y
Factor the expressions that are not already factored in \frac{x^{2}-y^{2}}{x-y}.
x+y-2x+y
Cancel out x-y in both numerator and denominator.
-x+y+y
Combine x and -2x to get -x.
-x+2y
Combine y and y to get 2y.
\frac{\left(x+y\right)\left(x-y\right)}{x-y}-2x+y
Factor the expressions that are not already factored in \frac{x^{2}-y^{2}}{x-y}.
x+y-2x+y
Cancel out x-y in both numerator and denominator.
-x+y+y
Combine x and -2x to get -x.
-x+2y
Combine y and y to get 2y.