text: # How do you solve x-4/x-1 = 12/3-x +1?
  
  ## solving rational equations
  
  Jul 20, 2018
  
  $x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$
  
  #### Explanation:
  
  $x - \frac{4}{x} - 1 = \frac{12}{3} - x + 1$ where $x \ne 0$
  
  $x - \frac{4}{x} - 1 = 4 - x + 1$
  
  $2 x - 6 = \frac{4}{x}$
  
  $2 {x}^{2} - 6 x = 4$
  
  $2 {x}^{2} - 6 x - 4 = 0$
  
  ${x}^{2} - 3 x - 2 = 0$
  
  $x = \frac{3 \pm \sqrt{9 + 8}}{2}$
  $x = \frac{3 \pm \sqrt{17}}{2}$
  $x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$
explanation: The document contains a math question and its corresponding answer. The question is about solving the equation \( x - \frac{4}{x-1} = \frac{12}{3-x} + 1 \), and the answer provides the solutions \( x = \frac{3 + \sqrt{17}}{2} \) or \( x = \frac{3 - \sqrt{17}}{2} \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # How do you solve x-4/x-1 = 12/3-x +1?
  
  ## solving rational equations
  
  Jul 20, 2018
  
  $x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$
  
  #### Explanation:
  
  $x - \frac{4}{x} - 1 = \frac{12}{3} - x + 1$ where $x \ne 0$
  
  $x - \frac{4}{x} - 1 = 4 - x + 1$
  
  $2 x - 6 = \frac{4}{x}$
  
  $2 {x}^{2} - 6 x = 4$
  
  $2 {x}^{2} - 6 x - 4 = 0$
  
  ${x}^{2} - 3 x - 2 = 0$
  
  $x = \frac{3 \pm \sqrt{9 + 8}}{2}$
  $x = \frac{3 \pm \sqrt{17}}{2}$
  $x = \frac{3 + \sqrt{17}}{2}$ or $x = \frac{3 - \sqrt{17}}{2}$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question is about solving the equation \( x - \frac{4}{x-1} = \frac{12}{3-x} + 1 \), and the answer provides the solutions \( x = \frac{3 + \sqrt{17}}{2} \) or \( x = \frac{3 - \sqrt{17}}{2} \).
  
  Label: question-and-answer