In this paper, the sum-rate maximization problem is studied for wireless networks that use downlink rate splitting multiple access (RSMA). In the considered model, each base station (BS) divides the messages that must be transmitted to its users into a `private' part and a `common' part. Here, the common message is a message that all users want to receive and the private message is a message that is dedicated to only a specific user. The RSMA mechanism enables a BS to adjust the split of common and private messages so as to control the interference by decoding and treating interference as noise and, thus optimizing the data rate of users. To maximize the users' sum-rate, the network can determine the rate allocation for the common message to meet the rate demand, and adjust the transmit power for the private message to reduce the interference. This problem is formulated as an optimization problem whose goal is to maximize the sum-rate of all users. To solve this nonconvex maximization problem, the optimal power used for transmitting the private message to the users is first obtained in closed form for a given rate allocation and common message power. Based on the optimal private message transmission power, the optimal rate allocation is then derived under a fixed common message transmission power. Subsequently, a one-dimensional search algorithm is proposed to obtain the optimal solution of common message transmission power. Simulation results show that the RSMA can achieve up to 15.6\% and 21.5\% gains in terms of data rate compared to non-orthogonal multiple access (NOMA) and orthogonal frequency-division multiple access (OFDMA), respectively.