OIMU 2010 Problem 3

A student adds up rational fractions incorrectly:

$$\frac{a}{b}+\frac{x}{y}=\frac{a+x}{b+y} (\star)$$

Despite that, he sometimes obtains correct results. For a given fraction $\frac{a}{b},a,b\in\mathbb{Z},b>0$ , find all fractions $\frac{x}{y},x,y\in\mathbb{Z},y>0$ such that the result obtained by $(\star)$ is correct.