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

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

Evaluate

$$-y$$

Short Solution Steps

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

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

Multiply \frac{\left(xy-x^{2}\right)xy}{x^{2}-2xy+y^{2}} times \frac{x-y}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

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

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

Extract the negative sign in -x+y.

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

Cancel out x-y in both numerator and denominator.

$$-y$$

Expand

$$-y$$

Short Solution Steps

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

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

Multiply \frac{\left(xy-x^{2}\right)xy}{x^{2}-2xy+y^{2}} times \frac{x-y}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

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

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

Extract the negative sign in -x+y.

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

Cancel out x-y in both numerator and denominator.

$$-y$$