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

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

Evaluate

$$y-x$$

Short Solution Steps

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

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

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

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

Do the multiplications in \left(xy-y\right)y-\left(xy-x\right)x.

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

Since \frac{xy^{2}-y^{2}-x^{2}y+x^{2}}{xy} and \frac{x^{2}-y^{2}}{xy} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

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

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

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

Cancel out xy in both numerator and denominator.

$$-x+y$$

Expand

$$y-x$$

Short Solution Steps

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

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

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

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

Do the multiplications in \left(xy-y\right)y-\left(xy-x\right)x.

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

Since \frac{xy^{2}-y^{2}-x^{2}y+x^{2}}{xy} and \frac{x^{2}-y^{2}}{xy} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

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

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

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

Cancel out xy in both numerator and denominator.

$$-x+y$$