consider the optimization problem of minimizing a raitonal function. we reformulate this problem as polynomial optimization by the technique of homogenization. these two problems are shown to be equivalent under some generic conditions. the exact jacobian sdp relaxation method is used to solve the reformulated problem. we also show that the convergence assumption of nonsingularity in jacobian sdp relaxation can be weakened as the finiteness of singularities. some numerical examples are given to show the efficiency of this method.