\(x = {1+\frac{\sqrt{2}}{1+\frac{\sqrt{2}}{1+...}}}\). 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 \(|A|+|B|+|C|\)?
