I believe I had that numerator and several others, but I settled on the one because it seemed to most clearly highlight the symmetry between the variables.
If you have not already done so then you might think about why there is this symmetry in the variables. It may be superficial and unimportant or there might be levels of enlightenment when you look at the reasons and consequences of the symmetry. I suppose there might even be a possibility of discovering other forms and perhaps even simpler forms to be found as a result. I'm not seeing any simpler forms yet.