Finding the ratio of acid and conjugate base from the absorbance equation

[![enter image description here](https://i.stack.imgur.com/VZrGn.png)](https://i.stack.imgur.com/VZrGn.png)


I am struggling on a question about acid dissociation constants.
Below is an image showing the problem but I will reiterate it here.
HX<->H+ + X-
Using the Beer-Law equation, derive that the ratio X- : HX is as follows:
A-A{HX}/A{X-}-A
Where A{HX} is the absorbance of the fully protonated solution
A{X-} is the absorbance of the fully deprotonated solution


My own attempts have been futile, for I keep getting:
epsilon{HX}(A-A{HX})/epsilon{X-}(A-A{X})
This equation would indicate that epsilon{HX}/epsilon{X-}=-1, which isn't possible
Any help would be appreciated


