solution: We can start by cross-multiplying: \begin{align*} 3\sqrt{3x-1}&=2\sqrt{2x}
  \\\Rightarrow \qquad (3\sqrt{3x-1})^2 &=(2\sqrt{2x})^2
  \\\Rightarrow \qquad 9(3x-1)& =4(2x)
  \\\Rightarrow \qquad 27x-9& =8x
  \\ \Rightarrow \qquad19x&=9
  \\ \Rightarrow \qquad x&=\boxed{\frac9{19}}.
  \end{align*}Checking, we see that this value of $x$ does indeed work, so it is not an extraneous solution.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  If $\frac{\sqrt{2x}}{\sqrt{3x-1}}=\frac32$, solve for $x$. Express your answer in simplest fractional form.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: \frac9{19}
extra_info.question: If $\frac{\sqrt{2x}}{\sqrt{3x-1}}=\frac32$, solve for $x$. Express your answer in simplest fractional form.
extra_info.split: test