This paper presents a novel approach to fractional programming (FP) for communication systems, focusing on power control and beamforming. The main contribution is a new quadratic transform technique that addresses multiple-ratio FP problems, which are more complex than single-ratio or max-min-ratio cases. The technique decouples the numerator and denominator of each ratio term, enabling the conversion of nonconvex problems into a sequence of convex problems. This allows for efficient iterative optimization with guaranteed convergence to a stationary point. The approach is applied to power control, beamforming, and energy efficiency maximization in wireless networks. The paper also demonstrates the connection between the proposed FP method and existing algorithms like fixed-point iteration and weighted minimum mean-square-error beamforming. The quadratic transform is shown to be effective in solving nonconvex optimization problems in communication systems, particularly in scenarios involving multiple signal-to-interference-plus-noise ratio (SINR) terms. The method is extended to multidimensional and complex cases, and its convergence rate is analyzed. The paper concludes that the proposed FP approach is competitive with state-of-the-art methods, with the closed-form FP variant offering lower computational complexity. The results show that the FP-based methods can achieve good performance in power control and beamforming for wireless communication systems.This paper presents a novel approach to fractional programming (FP) for communication systems, focusing on power control and beamforming. The main contribution is a new quadratic transform technique that addresses multiple-ratio FP problems, which are more complex than single-ratio or max-min-ratio cases. The technique decouples the numerator and denominator of each ratio term, enabling the conversion of nonconvex problems into a sequence of convex problems. This allows for efficient iterative optimization with guaranteed convergence to a stationary point. The approach is applied to power control, beamforming, and energy efficiency maximization in wireless networks. The paper also demonstrates the connection between the proposed FP method and existing algorithms like fixed-point iteration and weighted minimum mean-square-error beamforming. The quadratic transform is shown to be effective in solving nonconvex optimization problems in communication systems, particularly in scenarios involving multiple signal-to-interference-plus-noise ratio (SINR) terms. The method is extended to multidimensional and complex cases, and its convergence rate is analyzed. The paper concludes that the proposed FP approach is competitive with state-of-the-art methods, with the closed-form FP variant offering lower computational complexity. The results show that the FP-based methods can achieve good performance in power control and beamforming for wireless communication systems.