Is $x = \frac{a}{b} = \frac{b}{a/3}$ a continued fraction? How to solve for $x$?

Question

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

$x=9$

$x=\frac{1}{3}$

$x=3$

$x=\frac{1}{\sqrt3}$

$x={\sqrt3}$

Answer 1

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 $$x = \frac{a}{b} = \sqrt{3}$$

Answer 2

From this point $$x=\frac{a}{b}=\frac{3b}{a}$$ you can multiply everything by $ab$, giving $$abx = a^2 = 3b^2$$ Which is different from your next step.

Hint: if $x=\frac{a}{b}$, then what is $\frac{1}{x}$?