He watched TV rather than ___ his homework.
(A) did <parallel; Last night, he watched TV rather than did his homework.>
(B) do <but, Rather than do his homework, he watched TV. >
(C) doing <but, He watched TV instead of doing his homework.>
Rather than can also be used with nouns as a compound preposition meaning “instead of”: I bought a mountain bike rather than [buying] a ten-speed. But some people object to this use, insisting that than should be used only as a conjunction. They therefore object to constructions in which rather than is followed by a gerund, as in Rather than buying a new car, I kept my old one.
Clearly, it is grammatically defensible to follow rather than with a gerund, but if you prefer to avoid the controversy, use instead of with gerunds.
We ought to invest in new machinery rather than [invest in] buildings. (elliptical verb phrase)