Let P and Q be bounded linear operators on a Banach space. The existence of the Drazin inverse of P + Q is proved under some assumptions, and the representations of (P + Q) D are also given. The results recover the cases P 2 Q = 0, QPQ = 0 studied by Yang and Liu in [19] for matrices, Q 2 P = 0, PQP = 0 studied by Cvetković and Milovanović in [7] for operators and P 2 Q + QPQ = 0, P 3 Q = 0 studied by Shakoor, Yang and Ali in [16] for matrices. As an application, we give representations for the Drazin inverse of the operator matrix A =(a b / c d)