Решение:

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