How To express log(1+(x/(1+y)))

Hello,I’ve already looked at the problemCan CVX solve this kind of function {x-log(1+0.01*x/(x+1))} and I want to know if I could express the function log(1+(x/(1+y))) as fllow:
-rel_entr(-1,1+y) + log(-1-x-y)?
it seems that it could work in cvx , but I don’t know its result is right or wrong

At x = y = 1, one of the eigenvalues of the Hessian of log(1+(x/(1+y)) is negative, and the other is positive. Therefore, the function is neither convex nor concave, and can’t be used in CVX.

thank you so much,it helps me a lot