In this paper,we consider the Drazin inverse of a sum of two matrices andderive additive formulas under conditions weaker than those used in some recent papers on the subject. As a corollary we get the main results from the paper of Yang and Liu
[H.Yang,X.Liu,The Drazininverseofthesumoftwomatricesanditsapplications,J.Comput.Appl.Math.235 (2011) 1412–1417]. As an application we give some new representations for the Drazin inverseofablockmatrix.