((1+R)〖(-4+R^2)〗^2)/(4〖(6+4R+B^2 R-5R^2-R^3+R^4+B(-2+R+R^2))〗^2 )-((1+γ)〖(-4+γ^2)〗^2)/(9〖(6+4γ+β^2 γ-5γ^2-γ^3+γ^4+β(-2+γ+γ^2))〗^2 )>0, where 0 < γ < R < 1, 0 < β < B < 1. If you can give me some hints about proving it directly, that will be great. Or, Proving it with Mathematica is also ok. For example, I want to use the MinValue function. If the minimum value of the left is positive, then it is proven. But how to write the input with the constraint? So if you are familiar with Mathematica, please help! I really appreciate your time and help.