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Dual-Functional Radar-Communication (DFRC) is a promising paradigm to achieve Integrated Sensing and Communication (ISAC) in beyond 5G. In parallel, Rate-Splitting Multiple Access (RSMA), relying on multi-antenna Rate-Splitting (RS) by splitting messages into common and private streams at the transmitter and Successive Interference Cancellation (SIC) at the receivers, has emerged as a new strategy for multi-user multi-antenna communications systems. In this paper, we show that RSMA can be used as a unified and powerful multiple access and interference management strategy for multi-antenna DFRC system, where the base station has a dual communication and radar capability to simultaneously communicate with downlink users and probe detection signals to azimuth angles of interests. To that end, we design the message splits as well as the precoders of the communication (private and common) streams and radar sequence to jointly maximize the Weighted Sum Rate (WSR) and minimize the radar beampattern approximation Mean Square Error (MSE) subject to the per-antenna power constraint. We make key and refreshing observations. First, the proposed RSMA-assisted DFRC framework embraces existing DFRC frameworks based on Space-Division Multiple Access (SDMA) as subschemes. Second, RSMA exploits synergies in DFRC by making a better use of the common stream and the SIC receivers for the triple function of managing interference among communication users, managing interference between communication and radar, and enhancing radar sensing. Third, by contrasting with existing SDMA-based DFRC schemes where transmitting an additional radar sequence enhances the WSR-MSE tradeoff, RSMA-assisted DFRC frameworks with and without radar sequence achieve the same tradeoff performance and outperform all schemes using SDMA or orthogonal resources. Therefore, by enabling RSMA in DFRC, the system performance is enhanced and the system architecture is simplified since there is no need to use an additiona...