The fractional optimization is quite attractive and challenging from the viewpoint of the optimization theory and methods. And it arises in various economic applications as well as real-life problems, regardless of one ratio or the sum of several ratios are required to be optimized. While there are a lot of efficient algorithms for the single ratio case, less work has been devoted to solving the sum of ratios problems. In this talk, we consider two classes of fractional programming problems, the first case is the sum of linear ratios problem, and the second one is the sum of the generalized polynomial ratios problem with generalized polynomial constraints. For the first case, an approximation algorithm is presented and the computational cost of such an algorithm is given, besides, a new accelerating technique is introduced to improve the computational efficiency of the algorithm. For the second case, a practicable contraction approach is proposed and the novel equivalence transformation as well as contraction strategies are exhibited, then the solution of the original problem can be obtained through solving a series of standard geometric programming problems. Finally, the feasibility and effectiveness of these proposed algorithms are demonstrated by some numerical experiments.