In this article, we will implement a good comparison between three different paths of three different mathematical analysis tools in preparing to get the exact solution of the Generalized Hirota-Satsuma Coupling Korteweg De-Vries System which plays a vital role in hydrodynamics, fluid mechanics and physics. This model describes dispersive waves; specially the shallow water waves and has multiple soliton solutions and traveling wave solutions. The three important different techniques that included for this purpose are the Paul-Painlevé approach (PPAM) that usually achieve good results of the exact solution of all previously studied to NLPDE, the Ricatti-Bernolli Sub-ODE method (RBSODM) which is one of the famous ansatze approaches that doesn’t surrender to the balance rule and realize private results of the exact solution and the variational iteration method (VIM) which is one of interesting numerical methods that give a good results