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Rate-splitting (RS) has recently been recognized as a promising physical-layer technique for multi-antenna broadcast channels (BC). Due to its ability to partially decode the interference and partially treat the remaining interference as noise, RS is an enabler for a powerful multiple access, namely rate-splitting multiple access (RSMA), that has been shown to achieve higher spectral efficiency (SE) and energy efficiency (EE) than both space division multiple access (SDMA) and non-orthogonal multiple access (NOMA) in a wide range of user deployments and network loads. As SE maximization and EE maximization are two conflicting objectives, the study of the tradeoff between the two criteria is of particular interest. In this work, we address the SE-EE tradeoff by studying the joint SE and EE maximization problem of RSMA in multiple input single output (MISO) BC with rate-dependent circuit power consumption at the transmitter. To tackle the challenges coming from multiple objective functions and rate-dependent circuit power consumption, we first propose two methods to transform the original problem into a single-objective problem, namely, weighted-sum method and weighted-power method. A successive convex approximation (SCA)-based algorithm is then proposed to jointly optimize the precoders and RS message split of the transformed problem. Numerical results show that our algorithm converges much faster than existing algorithms. In addition, the performance of RS is superior to or equal to non-RS strategy in terms of both SE and EE and their tradeoff.