Problem:
If $x = \frac{3584}{2207}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{\sqrt{8082113}-1792}{2207}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/7927.txt'}