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

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

Evaluate

$$\frac{x^{2}-3xy+y^{2}}{x-y}$$

Short Solution Steps

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-y}{x-y}.

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

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

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

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

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

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

$$\frac{x^{2}+y^{2}-3xy}{x-y}$$

Expand

$$\frac{x^{2}-3xy+y^{2}}{x-y}$$

Short Solution Steps

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

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

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-y}{x-y}.

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

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

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

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

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

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

$$\frac{x^{2}+y^{2}-3xy}{x-y}$$