Problem:
If $x = \frac{301}{334}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{1}{668} \left(5 \sqrt{21473}-301\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/19126.txt'}