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

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

Evaluate

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

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}.

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

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

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

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

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

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

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

Differentiate w.r.t. x

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