Решение:

a) $$\left(\frac{x}{y^2} - \frac{1}{x}\right):\left(\frac{1}{y} + \frac{1}{x}\right) =$$ $$\left(\frac{x^2 - y^2}{xy^2}\right):\left(\frac{x + y}{xy}\right) =$$ $$\frac{(x - y)(x + y)}{xy^2} \cdot \frac{xy}{x + y} =$$ $$\frac{(x - y)}{y}$$

Ответ: $$\frac{x - y}{y}$$