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

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

Evaluate

$$y\left(y-x\right)$$

Short Solution Steps

Divide xy-x^{2} by \frac{x-y}{y} by multiplying xy-x^{2} by the reciprocal of \frac{x-y}{y}.

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

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

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

Extract the negative sign in y-x.

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

Cancel out x-y in both numerator and denominator.

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

Cancel out x and x.

$$-\left(x-y\right)y$$

Use the distributive property to multiply -1 by x-y.

$$\left(-x+y\right)y$$

Use the distributive property to multiply -x+y by y.

$$-xy+y^{2}$$

Expand

$$y^{2}-xy$$

Short Solution Steps

Divide xy-x^{2} by \frac{x-y}{y} by multiplying xy-x^{2} by the reciprocal of \frac{x-y}{y}.

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

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

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

Extract the negative sign in y-x.

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

Cancel out x-y in both numerator and denominator.

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

Cancel out x and x.

$$-\left(x-y\right)y$$

Use the distributive property to multiply -1 by x-y.

$$\left(-x+y\right)y$$

Use the distributive property to multiply -x+y by y.

$$-xy+y^{2}$$