Maximizing a Ratio/Percent

Question

I'm using cvxpy to model a problem.
Inside a very large and complex LP, I create two continuous, affine (unconstrained) expressions:x and y.
Due to how they are created, I know that 0 < x < y <= U. Obviously: x/y < 1.

In my LP objective, how do I maximize the ratio x/y?

Things I tried:

• Maximizing x*cp.inv_pos(Y) states my problem is non DCP (also if I try to minimize the inverse)
• I found various LP formulations for maximizing ratios (e.g. here or here) but these requires rewriting the constraints on all the terms in the expressions for x - I have no idea how to do that with cvxpy.
  If this is the way to go then an example would be very helpful!