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Given that the sum of the maximum and minimum value of
x4x8+2x6−4x4+8x2+16\frac{x^4}{x^8+2x^6-4x^4+8x^2+16}x8+2x6−4x4+8x2+16x4
can be expressed in the form pq\frac{p}{q}qp, where ppp and qqq are coprime, positive integers, find the value of p+qp+qp+q.
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