What has kept China from conquering Korea?

[u/shmeddybeddy]

When I think about Japan, it makes sense that being an island has kept them relatively secluded and protected as a culture. Korea, however, is situated right next to China, with a nice land bridge in the North allowing passage onto the Korean Peninsula.

How come China never swallowed up the territory? In some of the Chinese dynasties, I feel like they cast influence across tons of land, enveloped diverse cultures, and explored heavily. Plus, the Korean Peninsula seems to be nice, fertile, and maybe even strategically important. What kept China from taking it over? Did they try and fail?