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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?

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    $\begingroup$ 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}]. $\endgroup$ – J. M. is away Mar 31 at 10:45
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Simply use

Assuming[0 < d < e < 1, FullSimplify[expr1 > expr2]]
(* True *)
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