When you have several area rugs in a common space, the simplest approach is to use matching rugs. This separates the spaces but keeps the feeling harmonious. In this example, the areas serve the same function, so there's no need to create a great distinction between them.
Matching area rugs can feel a bit predictable and safe. Using an unusual rug is one way to avoid that problem. Here a bold graphic is repeated on both sides of the room. The repetition helps to temper the high-contrast pattern so it doesn't overwhelm the space.
Two different floor coverings were used in this interior to help distinguish the dining area from the living area. The rugs share a similar color palette, assuring harmony.
One rug is patterned; the other is solid. But they look great together, because they share a common color.
It's easier to combine solid carpets than patterned ones. Just choose two colors that look good together, like this pair. Pairing is always easier when one of the carpets is a neutral.
Although these two area rugs are very different, they're compatible because they share a similar color palette. They also share a similar sensibility, which is nearly as important. Had one been a modern geometric or overtly lower in quality than the other, this wouldn't have worked as well.
Oriental rugs can be easier to combine than other carpets, because they often share a common sensibility and color palette, and the patterns are so detailed, they're less likely to clash with other patterns. The mix works best when there's a common dominant color, as in this yellow-based pair.