The Rare Isotope Accelerator of Newness (RAON) accelerator is under construction to generate and accelerate the stable ion beams and the rare isotope beams for various kinds of experiment programs. Especially, the post accelerator section was designed to be able to separately accelerate and transport the stable ion beams created by the superconducting electron cyclotron resonance ion source (ECR-IS) and the rare isotope beams created by the Isotope Separation On-Line (ISOL) system. However, recently, the research of the simultaneous operation of the stable ion beams and the rare isotope beams has been conducted to more efficiently satisfy the a wide range of beam requirements of the experimental halls. For the operation, we has modified the lattice of the post low energy beam transport (LEBT) section for the injection of the rare isotope beam and the next lattice after the low energy superconducting linac (SCL3) section for the extraction of the accelerated beam in the post accelerator section of the RAON accelerator. In this paper, the new lattice designs of the injection and extraction parts will be presented and we will describe the results of the beam dynamics simulations for the simultaneous operation of the two kinds of beams.