Frightful Fraction Minimization

Algebra Level 4

Given non-zero real values of \(a,b\) and \(c\) such that their sum is \(x\), we denote \(f(x) \) as the minimum value of \( 3 + \frac{a+b}c+ \frac{b+c}a+\frac{c+a}b \). If \(f(x) = 9 \) for all integers \(-10\le x \le 10 \) except at \(x=P \), find the value of \(P\).

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