In this talk, we will focus on the optimization problem of minimizing a sum of rational functions over a basic semialgebraic set. We provide a hierarchy of semidefinite relaxations that is dual to the generalized moment problem (GMP) approach due to Bugarin, Henrion, and Lasserre. The exploration of the dual aspect not only allows us to conduct a convergence rate analysis, but also leads to a sign symmetry adapted hierarchy of semidefinite relaxations. Moreover, we further reduce the complexity of semidefinite relaxations by exploiting both correlative sparsity and sign symmetries. Numerical experiments demonstrate the efficiency of our approach.