An algebra problem by Krishna Sharma

Algebra Level 5

Given that the sum of the maximum and minimum value of

\[\frac{x^4}{x^8+2x^6-4x^4+8x^2+16}\]

can be expressed in the form \(\frac{p}{q}\), where \(p\) and \(q\) are coprime, positive integers, find the value of \(p+q\).

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