Given that \(x = {1+\frac{\sqrt{2}}{1+\frac{\sqrt{2}}{1+...}}}\), find \(\frac{1}{(x+1)(x-2)}\).
When your answer is in the form \(\frac{A+\sqrt{B}}{C}\), where A, B, and C are integers, and B is not divisible by the square of a prime, what is |A|+|B|+|C|?
