Solve x/x+y-x+y

$$\frac { x } { x + y } - x + y$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Differentiate w.r.t. x

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