text: ## 85295james 3 years ago Simplify the rational expression. State any excluded values.
  
  1. 85295james
  
  x-2/x^2+3x-10
  
  2. mathslover
  
  is this the question? : $\large{\frac{x-2}{x^2+3x-10}}$ ?
  
  3. 85295james
  
  yes that is it
  
  4. KingGeorge
  
  Can you factor the denominator?
  
  5. 85295james
  
  what do you mean ??
  
  6. 85295james
  
  x=-5 or x=2
  
  7. KingGeorge
  
  Right. So that means $$x^2+3x-10=(x+5)(x-2)$$. That means your rational expression becomes$\frac{(x-2)}{(x+5)(x-2)}$Before we go farther, can you tell me what the excluded values will be?
  
  8. 85295james
  
  i dont know :(
  
  9. KingGeorge
  
  The excluded values are the zeroes of the denominator. So you get $$x=-5,2$$. Now I'm sure that you can simplify it.
  
  10. 85295james
  
  so x=0
  
  11. KingGeorge
  
  You have excluded values when your denominator is 0. Also, I've got to go now. If you have questions, I'll be back on later tonight, so I can answer your questions then.
  
  12. 85295james
  
  so x2
  
  13. KingGeorge
  
  Do you mean $$x^2$$?
  
  14. 85295james
  
  no
  
  15. KingGeorge
  
  x=2?
  
  16. KingGeorge
  
  I'm a bit confused. Are you stuck with the simplification or the excluded values?
  
  17. 85295james
  
  sorry one secc
  
  18. 85295james
  
  |dw:1346987271707:dw|
  
  19. 85295james
  
  i dont think it is (A) now
  
  20. 85295james
  
  (C)????
  
  21. KingGeorge
  
  It is not C. Look back at the equation. $\frac{(x-2)}{(x+5)(x-2)}$How can you simplify this?
  
  22. 85295james
  
  no
  
  23. KingGeorge
  
  $\frac{\cancel{(x-2)}}{(x+5)\cancel{(x-2)}}$What do you get?
  
  24. 85295james
  
  (B)
  
  25. KingGeorge
  
  no...You should get $\frac{1}{(x+5)}$
  
  26. 85295james
  
  o lol (D)
explanation: The document is a conversation between a user and a math tutor, discussing the simplification of a rational expression. The user initially presents the problem, and the tutor guides the user through the steps to solve it. The conversation includes a question and an answer.
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: ## 85295james 3 years ago Simplify the rational expression. State any excluded values.
  
  1. 85295james
  
  x-2/x^2+3x-10
  
  2. mathslover
  
  is this the question? : $\large{\frac{x-2}{x^2+3x-10}}$ ?
  
  3. 85295james
  
  yes that is it
  
  4. KingGeorge
  
  Can you factor the denominator?
  
  5. 85295james
  
  what do you mean ??
  
  6. 85295james
  
  x=-5 or x=2
  
  7. KingGeorge
  
  Right. So that means $$x^2+3x-10=(x+5)(x-2)$$. That means your rational expression becomes$\frac{(x-2)}{(x+5)(x-2)}$Before we go farther, can you tell me what the excluded values will be?
  
  8. 85295james
  
  i dont know :(
  
  9. KingGeorge
  
  The excluded values are the zeroes of the denominator. So you get $$x=-5,2$$. Now I'm sure that you can simplify it.
  
  10. 85295james
  
  so x=0
  
  11. KingGeorge
  
  You have excluded values when your denominator is 0. Also, I've got to go now. If you have questions, I'll be back on later tonight, so I can answer your questions then.
  
  12. 85295james
  
  so x2
  
  13. KingGeorge
  
  Do you mean $$x^2$$?
  
  14. 85295james
  
  no
  
  15. KingGeorge
  
  x=2?
  
  16. KingGeorge
  
  I'm a bit confused. Are you stuck with the simplification or the excluded values?
  
  17. 85295james
  
  sorry one secc
  
  18. 85295james
  
  |dw:1346987271707:dw|
  
  19. 85295james
  
  i dont think it is (A) now
  
  20. 85295james
  
  (C)????
  
  21. KingGeorge
  
  It is not C. Look back at the equation. $\frac{(x-2)}{(x+5)(x-2)}$How can you simplify this?
  
  22. 85295james
  
  no
  
  23. KingGeorge
  
  $\frac{\cancel{(x-2)}}{(x+5)\cancel{(x-2)}}$What do you get?
  
  24. 85295james
  
  (B)
  
  25. KingGeorge
  
  no...You should get $\frac{1}{(x+5)}$
  
  26. 85295james
  
  o lol (D)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a conversation between a user and a math tutor, discussing the simplification of a rational expression. The user initially presents the problem, and the tutor guides the user through the steps to solve it. The conversation includes a question and an answer.
  
  Label: question-and-answer