Problem:
If $x = \frac{2975}{5302}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{\sqrt{121295441}-2975}{10604}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/14381.txt'}