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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Differentiate w.r.t. x

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