Solve xy/x^2-y^2*(x/y-y/x)

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

Evaluate

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Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and x is xy. Multiply \frac{x}{y} times \frac{x}{x}. Multiply \frac{y}{x} times \frac{y}{y}.

$$\frac{xy}{x^{2}-y^{2}}\left(\frac{xx}{xy}-\frac{yy}{xy}\right)$$

Since \frac{xx}{xy} and \frac{yy}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xy}{x^{2}-y^{2}}\times \frac{xx-yy}{xy}$$

Do the multiplications in xx-yy.

$$\frac{xy}{x^{2}-y^{2}}\times \frac{x^{2}-y^{2}}{xy}$$

Multiply \frac{xy}{x^{2}-y^{2}} times \frac{x^{2}-y^{2}}{xy} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out xy\left(x^{2}-y^{2}\right) in both numerator and denominator.

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Factor

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