Problem:
If $x = \frac{12286}{2239}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{\sqrt{42749570}-6143}{2239}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/20104.txt'}