An algebra problem by Krishna Sharma

Algebra Level 5

Given that the sum of the maximum and minimum value of

x4x8+2x64x4+8x2+16\frac{x^4}{x^8+2x^6-4x^4+8x^2+16}

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

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