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$x = 1 + \cfrac{\sqrt{3}}{1 + \cfrac{\sqrt{3}}{1 + \dotsb}}$. Find $\frac{1}{(x + 2)(x - 1)}$. 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,

 Oct 28, 2022
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The answer is (-2 + sqrt(6))/5.

 Oct 28, 2022

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