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Algebraic Continued Fraction

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The first part develops the fraction from a simple equation or statement with a single unknown variable and demonstrates the recursive, iterative procedure. Possibly as simple and straightforward as it is possible for me to do. The second part still confuses me and amounts to no mare than an exercise in fitting such information on a small screen device.
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See Also:
Copyright Information - Where Appropriate:
CCBY
Attribution 4.0 International (CC BY 4.0)
CCBY SA
Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)
PD
Public Domain
FU
Fair Use