We derive an exact expression for the transmission coefficient through an Aharonov-Bohm ring with a side-coupled quantum dot using the scattering-matrix approach. We show a sudden AB phase change by π as the quantum dot is tuned across the resonance. The Aharonov-Bohm oscillation amplitude can be modulated effectively by tuning the quantum dot level. The transmission coefficient has an expression of the generalized Fano form with a complex Fano parameter q in the presence of the Aharonov-Bohm flux.