<s>[INST] 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? 
 [/INST] Here is a solution  ; sorry for hand writing 
$$\begin{align*}
\frac{1}{a+\frac{1}{b+\frac{1}{c+1}}}&=\frac{16}{38}\\
a+\frac{1}{b+\frac{1}{c+1}}&=\frac{38}{16}= 2+\frac{3}{8}\\
\text{So}\quad      a=2\\
\frac{1}{b+\frac{1}{c+1}}&=\frac{3}{8}\\
b+\frac{1}{c+1}&=\frac{8}{3}=2+\frac{2}{3}\\
\text{So}\quad     b=2\\
\frac{1}{c+1}&=\frac{2}{3}\\
c+1=\frac{3}{2}=1+\frac{1}{2}\\
\text{So}\quad     c=\frac{1}{2}\\
\end{align*}$$
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