Решение №4

Упростим выражение:

$$\left(\frac{x + y}{y} - \frac{4x}{x+y}\right) \cdot \frac{xy + y^2}{x-y} =$$ $$\left(\frac{(x + y)(x+y) - 4x \cdot y}{y(x+y)}\right) \cdot \frac{y(x + y)}{x-y} =$$ $$\frac{x^2 + 2xy + y^2 - 4xy}{y(x+y)} \cdot \frac{y(x+y)}{x-y} =$$ $$\frac{x^2 - 2xy + y^2}{y(x+y)} \cdot \frac{y(x+y)}{x-y} =$$ $$\frac{(x - y)^2}{y(x+y)} \cdot \frac{y(x+y)}{x-y} =$$ $$\frac{(x - y)^2 \cdot y(x+y)}{y(x+y) \cdot (x-y)} = x-y$$

Ответ: $$x-y$$