Решение:

$$\frac{y^2-x^2}{x^2-2xy+y^2} = \frac{(y-x)(y+x)}{(x-y)^2} = \frac{(-1)(x-y)(y+x)}{(x-y)(x-y)} = -\frac{x+y}{x-y}$$

Ответ: $$\frac{-(x+y)}{x-y}$$