We just have to factorise it. It's so simple! Or is it?

Algebra Level 3

\[\left| \frac { { x }^{ 2 }-3x-1 }{ { x }^{ 2 }+x+1 } \right| \ge 3\\ \\ A=\max { (x) } \\ B=\min { (x) } \\ \]

Find \(AB\left( A-B \right) \).

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