Problem:
If $x = \frac{13438}{20383}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{5 \sqrt{18424466}-6719}{20383}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/30272.txt'}