Is it correct grammar to say you would rather dance than sing?

Yes, the sentence "You would rather dance than sing" is grammatically correct. It uses the correct form of "would rather" followed by a verb in the base form.

Here's why it works:

* "Would rather" expresses a preference.

* "Dance" and "sing" are both verbs in their base form, which is the correct form to use after "would rather."

The sentence indicates that the person prefers dancing over singing.