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

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

Evaluate

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Short Solution Steps

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

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

Cancel out x in both numerator and denominator.

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

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

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

Since \frac{x^{2}-y^{2}}{y\left(x-y\right)} and \frac{x\left(x-y\right)}{y\left(x-y\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-y^{2}-x\left(x-y\right).

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

Combine like terms in x^{2}-y^{2}-x^{2}+xy.

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

Factor the expressions that are not already factored in \frac{xy-y^{2}}{y\left(x-y\right)}.

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

Cancel out y\left(x-y\right) in both numerator and denominator.

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Factor

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