Presuming A>= 0, the same basic idea can be used, with some extra complication: The expression after the lattermost = can be entered in CVX
x*log(1+y/(x+A)) = (x+A)*log(1+y/(x+A)) - A*log(1+y/(x+A))
= -rel_entr(x+A,x+A+y) - A*(rel_entr((x+A)/y,(x+A)/y+1) + rel_entr((x+A)/y+1,(x+A)/y))
If x and y are both variables, the decomposition in the first line does not result in a formulation which can be entered in CVX, although it is still mathematically correct. That is because A*log(1+y/(x+A) is neither convex nor concave jointly in x; and y, and therefore can;'t be reformulated for CVX, even though x*log(1+y/(x+A)) is jointly concave in x and y.