Integrating intelligent reflecting surface (IRS) and Rate-Splitting Multiple Access (RSMA) is an effective solution to improve the spectral/energy efficiency in next-generation (beyond 5G (B5G) and 6G) wireless networks. In this paper, we investigate a rate-splitting (RS)-based transmission technique for an IRS-aided communication network involving both near and cell-edge users. In particular, we derive a new architecture called IRS-RS that leverages the interplay between RS and IRS, with an aim to maximize the weighted sum-rate (WSR) of users by selecting the reflecting coefficients at the IRS and designing beamformers at the BS under the constraints of power at the base station (BS), quality of service (QoS) at each user and finite resolution at the IRS. To solve the non-convex WSR maximization problem, we propose an alternating algorithm and compare its performance with baseline non-orthogonal multiple access (NOMA) based transmission for an IRS-aided communication network for both perfect and imperfect CSIT cases. Through numerical results, it is shown that the proposed IRS-RS architecture yields better QoS with respect to the cell-edge users when compared to IRS-NOMA transmission scheme.