Problem:
If $x = \frac{114}{61}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{1}{61} \left(\sqrt{6970}-57\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/214.txt'}