<s>[INST] Is $x = \frac{a}{b} = \frac{b}{a/3}$ a continued fraction? How to solve for $x$? I believe following is a continued fraction. I'm stumped on how to solve for x
$x = \frac{a}{b} = \frac{b}{a/3}$
I know it can be re-written as 
$x = \frac{a}{b} = \frac{3b}{a}$
$x = a^2 = 3b^2$
I'm unsure where to go from here.
Below are the choices
$x=9$
$x=\frac{1}{3}$
$x=3$
$x=\frac{1}{\sqrt3}$
$x={\sqrt3}$
 [/INST] The part where you wrote $x=a^2=3b^2$ is not correct. 
From $$ \frac{a}{b} = \frac{b}{a/3} \implies a^2/3 = b^2 \implies a^2=3b^2$$
So $a = \sqrt{3}b$ and thus $$x = \frac{a}{b} = \sqrt{3}$$
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