Is "in" missing here?

[Rei]

The teacher explained to the students the relationship between animals and the places they live.

This is a sentence from the textbook I use.
I think the last part should be "places they live in".
Is this sentence right, or should I add an "in"?

Thanks in advance.

[Dozy]

I see "places they live" as an abbreviation of "places where / in which they live", rather than an abbreviation of "places they live in". I find it acceptable, though in formal writing I think I would use the full version. "places they live in" would also be OK of course.

Similar examples: "go back to the place you belong", "this is the place it appeared", etc.