+140 Let \(x = {1+\frac{\sqrt{2}}{1+\frac{\sqrt{2}}{1+ \dotsb}}}.\)
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 \(|A|+|B|+|C|\)?
