Find a,b and c. Any method? Given that $$\frac{1}{a+\frac{1}{b+\frac{1}{c+1}}}=\frac{16}{38}$$, find $a,b,c$.
I've been figuring for this quite some time? Is it possible to solve? 

Sure it is, but you'll end up with infinite possibilities:
$$\begin{align*}
\frac{1}{a+\frac{1}{b+\frac{1}{c+1}}}&=\frac{16}{38}\\
a+\frac{1}{b+\frac{1}{c+1}}&=\frac{38}{16}\\
\frac{1}{b+\frac{1}{c+1}}&=\frac{38-16a}{16}\\
b+\frac{1}{c+1}&=\frac{16}{38-16a}\\
\frac{1}{c+1}&=\frac{16-(38-16a)b}{38-16a}\\
c&=\frac{38-16a}{16-(38-16a)b}-1
\end{align*}$$
You can chose $a$ and $b$ freely, and then $c$ will be determined by the two.
