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 $x = \frac{3 - \sqrt{17}}{2}$