I want to solve the following optimization problem:

\eqalign{\max_x\quad & (1-x) \log_2 \left(1+ \underbrace{\left(\frac{xD - (1-x)E}{(1-x)F+(1-x)G}\right)}_A\right)}

Such that P_1<x\leq P_2 where, D, E, F, G, P_1, and P_2 are positive real numbers.

**My attempted solution:**

Since at higher values of A it is also possible to approximate the logarithmic function to

(1-x) \log_2 \left(1+ \left(\frac{xD - (1-x)E}{(1-x)F+(1-x)G}\right)\right) \approx (1-x) \log_2 \left(\frac{xD - (1-x)E}{(1-x)F+(1-x)G}\right)

I tried to solve the inner part, i.e., \left(A=\frac{xD - (1-x)E}{(1-x)F+(1-x)G}\right) using fractional programing (such as Dinkelbach Algorithm), but I am not sure how to tackle this problem as a whole in CVX.

Any kind of help in this regard will be very much appreciated.