Roots of a Quartic

Algebra Level 4

Let \(r_1,r_2,r_3,r_4\) be roots of the polynomial \(x^4-4x^3+6x^2+8x+10\).

\[\dfrac{1}{r_2+r_3+r_4}+\dfrac{1}{r_1+r_3+r_4}+\dfrac{1}{r_1+r_2+r_4}+\dfrac{1}{r_1+r_2+r_3}=\dfrac{A}{B}\]

where \(A\) and \(B\) are co-prime positive integers. Find \(A+B\).

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