Comparison of variables

[gerlindemientus]

Hi there,
I have a little problem. I want to compare expr1 and expr2 with each other and find conditions under which expr1 is greater than expr2. I researched that Reduce would do the job here, BUT each expression consists of four variables {c,beta,FA,FB}. Now I want to find the conditions for c and beta and incorporate tha fact that I already assumed FA>FB. How can I achieve that?
Here are the explicit expressions:
ReduceB

Reduce[(2 (6 (-1 + c)^2 (1 + \[Beta]) (2 + \[Beta]) - (8 + 
        5 \[Beta])^2 Subscript[F, A] - (8 + 5 \[Beta])^2 Subscript[F, 
      B]))/(8 + 5 \[Beta])^2 > (1/(
  32 (8 + \[Beta] (7 + \[Beta]))^2))((-1 + 
       c)^2 (1 + \[Beta]) (768 + \[Beta] (704 + \[Beta] (182 + 
             15 \[Beta]))) - 
    32 (8 + \[Beta] (7 + \[Beta]))^2 Subscript[F, A] - 
    64 (8 + \[Beta] (7 + \[Beta]))^2 Subscript[F, B]), {c, \[Beta]}, 
 Subscript[F, A] > Subscript[F, B]]

Thanks for your help.
PS: Sorry for the bad formation did not find a way to improve it ;).

[shenghuiy (Shenghui Yang)]

Here is your result. It is not very pleasant to read because large spew of the root objects from Mathematica trying to symbolically handle the roots of the polynomial involved.

The code is attached in the following notebook. You need && to combine the expression and the conditions.

[gerlindemientus]

Thanks a lot for the immediate respond. I really appreciate it.