The prohibition of Borer applies only when there are two items mixed together; if the items are not mixed, but simply next to each other, it is not forbidden to separate them. For example, if walnuts and peanuts are mixed together and one wishes to eat the walnuts immediately, he may take the walnuts out of the mixture, but he may not remove the peanuts. In contrast, if they are next to each other, he may remove all of the peanuts in order to serve the walnuts. Since they are not mixed together, Borer does not apply.
Borer does apply to pieces of different kinds of fish that are mixed together. Following the rules established above, one may remove the pieces one wishes to eat immediately, but one may not remove the pieces one does not wish to eat. Even if the pieces are large, if they are mixed together and it takes effort to find the type he wants, Borer applies, as the pieces he does not want are considered psolet for him. However, if all the pieces of the type of fish he wants are at the bottom of a serving dish, he may remove the top pieces to get to the bottom ones. Since they are arranged such that one type of food is on top and the other is below, separating them is not considered Borer (Rema 319:3; BHL s.v. “le’ekhol miyad”; see SSK ch. 3 n. 7).
Does Borer apply to a mixture of plums and peaches? If there are only a few pieces of fruit, since they are large, they are not considered mixed together, and one may separate them in any way he desires. But if there are many fruits, they are considered mixed, and the laws of Borer apply. Thus, one may not separate them through derekh melakha, but he may take the fruit that he wishes to eat immediately, as that is derekh akhila.
If a pot of soup contains small pieces of chicken or vegetables, since the pieces are small and it is difficult to remove them, the prohibition of Borer applies. This means that one may remove the pieces from the soup and eat them immediately, but he may not remove them from the soup in order to eat the soup without them. In addition, he may not remove them in order to eat them later. But if there are large pieces of meat in the soup, since it is not difficult to search for them and remove them, they are not considered mixed with the soup, and thus Borer does not apply. Therefore, one may remove the pieces from the soup in order to eat the soup by itself, or to eat them later. This is also the case with matza balls in clear soup, as they are not considered mixed with the soup.