To simplify the expression \(\frac{2y^2 - 2xy}{x^2 - y^2}\), we can follow these steps:
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Factor the numerator: The numerator \(2y^2 - 2xy\) can be factored by taking out the common factor \(2y\):
\[ 2y^2 - 2xy = 2y(y - x) \]
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Factor the denominator: The denominator \(x^2 - y^2\) is a difference of squares, which can be factored as:
\[ x^2 - y^2 = (x - y)(x + y) \]
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Rewriting the expression: Substituting the factored forms back into the expression gives:
\[ \frac{2y(y - x)}{(x - y)(x + y)} \]
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Simplifying the expression: Notice that \((y - x) = -(x - y)\), so we can rewrite the numerator:
\[ 2y(y - x) = -2y(x - y) \]
Therefore, we have:
\[ \frac{-2y(x - y)}{(x - y)(x + y)} \]
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Cancel the common factor: Assuming \(x \neq y\), we can cancel out \((x - y)\) from the numerator and denominator:
\[ = \frac{-2y}{x + y} \]
Thus, the simplest form of the expression \( \frac{2y^2 - 2xy}{x^2 - y^2} \) is:
\[ \boxed{\frac{-2y}{x+y}} \] (for \(x \neq y\)).