Problem:
If $x = \frac{30890}{30419}$, then find $\frac{1}{x+\frac{1}{x+\frac{1}{x+\ddots}}}$.
Answer:
$\frac{\sqrt{1163863586}-15445}{30419}$
{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/continued_fraction/44481.txt'}