Question: How to extract the numerators of equations and simplify them?

I have a system of 3 (very large) nonlinear equations in 3 variables. Since I cannot feed non-algebraic expressions into polynomial solvers, I want to extract only their numerators (which should be algebraic) and solve the three numerators for the 3 variables. These solutions should also solve the non-algebraic system then. 

This is the original system (sorry I don't know why but I was not able to include the massive expression in the startup code):

I think I am not understanding the syntax. To extract the numerators, I am using ((numer@evala@:-Norm@numer)~@eval)(Eqs) (scroll down to the very bottom of my script):

  1. Am I wrong?
  2. What exactly am I doing with this combined command?
  3. Why length(((numer@evala@:-Norm@numer)~@eval)(Eqs)) is much larger than length(Eqs)? Shouldn't it be smaller since I just extract the numerators?

Thank you.

Please Wait...