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2025 SSMO Accuracy Round Problems/Problem 4

Problem

Let $a,$ $b,$ and $c$ be the roots of the polynomial $x^3+4x^2-3x-4$. Suppose that \[\left|\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\right|=\frac{m}{n},\] for relatively prime positive integers $m$ and $n$. Find $m+n$.

Solution

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