Reduce (x-y)/(x^2-2xy+y^2)

$\frac{x - y}{x^{2} - 2 x y + y^{2}}$

Factor using the perfect square rule.

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Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot x \cdot (- y)$

Simplify.

$2 a b = - 2 x y$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = - y$ .

$\frac{x - y}{{(x - y)}^{2}}$

Cancel the common factor of $x - y$ and ${(x - y)}^{2}$ .

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Multiply by $1$ .

$\frac{(x - y) \cdot 1}{{(x - y)}^{2}}$

Cancel the common factors.

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Factor $x - y$ out of ${(x - y)}^{2}$ .

$\frac{(x - y) \cdot 1}{(x - y) (x - y)}$

Cancel the common factor.

$\frac{(x - y) \cdot 1}{(x - y) (x - y)}$

Rewrite the expression.

$\frac{1}{x - y}$

Reduce (x-y)/(x^2-2xy+y^2)

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