This paper investigates rate-splitting (RS) precoding for non-orthogonal unicast and multicast (NOUM) transmissions using fully-digital and hybrid precoders. We study the nonconvex weighted sum-rate (WSR) maximization problem subject to a multicast requirement. We propose FALCON, an approach based on sequential parametric optimization, to solve the aforementioned problem. We show that FALCON converges to a local optimum without requiring judicious selection of an initial feasible point. Besides, we show through simulations that by leveraging RS, hybrid precoders can attain nearly the same performance as their fully-digital counterparts under certain specific settings.