# Testing which expression is greater

I have two expressions:

expr1 = e^2/(8 + 4*e + e^2)


and

expr2 = (d^2 - 2*d*e + e^2)/(8 + d^2 - 2*d*2 - 2*d*e + 4*e + e^2)


and one inequality:

0 < d < e < 1


I need to decide which expression is greater, and if one is not always greater, under what circumstances they change order. Equally, is it a decidable question?

• Try CylindricalDecomposition[0 < d < e < 1 && e^2/(8 + 4*e + e^2) < (d^2 - 2*d*e + e^2)/(8 + d^2 - 2*d*2 - 2*d*e + 4*e + e^2), {d, e}]. – J. M. is away Mar 31 at 10:45

Assuming[0 < d < e < 1, FullSimplify[expr1 > expr2]]