Problem:
If $x = \frac{11000}{3007}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{\sqrt{39292049}-5500}{3007}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/22164.txt'}