That function is neither convex nor concave, and therefore will not be accepted by CVX.
f = (a*log(a)+b*log(b)) / (a+b)
The Hessian evaluated at a = b = 1 has eigenvalues -1/2 and 1/2, so is indefinite at that point.
Edit: I misread your parentheses. I’m guessing that the preceding part of my answer is what you really meant. Nevertheless, I will show the conclusion is the same with the parentheses literally as you wrote them.
f = a/(a+b)*log(a/(a+b)) + b/(a+b)*log(b/(a+b))
The Hessian evaluated at a = 1, b = 2 has eigenvalues -0.0171306101 and 0.3462526235, so is indefinite at that point.