<s>[INST] Question in fraction (not simple ) I have a question and its answer but I don't know how can i solve 
$$\frac {37}{13} = 2+ \frac {1}{x+\frac{1}{5+\frac{1}{y}}} $$
the answer $ x =1, y=2$
Could any one explain how to solve this ?? please 
 [/INST] This is a development in continued fraction.
At each step, you have to compute a quotient and remainder, like this:
$\frac{37}{13}$ has quotient $2$ and remainder $11$, thus $37=13 \times 2 + 11$, or also$\frac{37}{13}=2+\frac{11}{13}=2+\dfrac{1}{\dfrac{13}{11}}$.
Now you do the same with $\frac{13}{11}=1+\frac{2}{11}$, thus
$$\frac{37}{13}=2+\dfrac{1}{1+\dfrac{2}{11}}=2+\dfrac{1}{1+\dfrac{1}{\dfrac{11}{2}}}$$
And finally, $\dfrac{11}{2}=5+\dfrac{1}{2}$, thus
$$\frac{37}{13}=2+\dfrac{1}{1+\dfrac{1}{5+\dfrac{1}{2}}}$$
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