Learn German: Das Krankenhaus ist neben dem Schwimmbad. - The hospital is next to the swimming pool.

The word neben (next to) is a two-way preposition. It takes the dative case when it describes a fixed location answering the question "where?" (wo?). Since the hospital is just sitting there and not moving to a new location, we change the neuter das Schwimmbad to the dative form dem Schwimmbad.

How do we know the gender of compound words like Krankenhaus and Schwimmbad?

The gender of a German compound noun always matches its very last part. Krankenhaus ends with das Haus (the house) and Schwimmbad ends with das Bad (the bath or pool). Because both end in a neuter noun, both compound words use das.

Would we ever say neben das Schwimmbad?

Yes, if there was movement toward a destination. Two-way prepositions take the accusative case when answering "where to?" (wohin?). If someone were building or moving a hospital to be next to the pool, you would use the accusative das Schwimmbad. But here, it describes a static location, so we use the dative.

Can I combine neben dem into a short word like we do with im or am?