Solve x-y+4xy/x-y

$$x-y+ \frac{ 4xy }{ x-y }$$

Evaluate

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

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}.

$$\frac{\left(x-y\right)\left(x-y\right)}{x-y}+\frac{4xy}{x-y}$$

Since \frac{\left(x-y\right)\left(x-y\right)}{x-y} and \frac{4xy}{x-y} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-y\right)\left(x-y\right)+4xy}{x-y}$$

Do the multiplications in \left(x-y\right)\left(x-y\right)+4xy.

$$\frac{x^{2}-xy-xy+y^{2}+4xy}{x-y}$$

Combine like terms in x^{2}-xy-xy+y^{2}+4xy.

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

Differentiate w.r.t. x

$$\frac{\left(x-3y\right)\left(x+y\right)}{\left(x-y\right)^{2}}$$