Normally the sum of ratios problems are reduced into a sequence of single-ratio problems and then solved by existing methods. Because of their combinatorial nature, the computational complexity grows exponentially. A sum of nonlinear fractional function optimization problem with several fractions is proved to be a NP-complete problem indicating that an efficient algorithm may not exist. The non-linear sum of fractional functions are linearized by piecewise linearization technique and converted into a linear sum of fractional programming problem. Optimal solution is found at for the new problem. The number of iterations depends on the contribution of decision variables to objective function value.