Решение:

$$\frac{x^2-y^2}{y+z}:\frac{y^2+xy}{y^2-z^2} = \frac{(x-y)(x+y)}{y+z} \cdot \frac{(y-z)(y+z)}{y(y+x)} = \frac{(x-y)(y-z)}{y}$$

Ответ: $$\frac{(x-y)(y-z)}{y}$$