# 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 $$P$$.

×