text: # Fractions . Simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)].
  
  ## Expert Answers
  
  We need to simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]
  
  [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]
  
  use x^2 - 4 = (x - 2)(x +2), also let's find the factors of x^2+3x+2
  
  => [(x^2 + 2x + x +2)/(x-2)]*[(x - 2)(x + 2)/(x-1)]
  
  => [(x + 2)(x + 1)/(x - 2)]*[(x - 2)(x + 2)/(x-1)]
  
  cancel the common terms in the numerator and denominator
  
  => (x + 2)^2*(x + 1)/(x - 1)
  
  The simplified form of the given expression is (x + 2)^2*(x + 1)/(x - 1)
  
  Approved by eNotes Editorial Team
explanation: The document contains a math question asking for the simplification of a given algebraic expression involving fractions. It also includes a detailed step-by-step solution to the problem.
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: # Fractions . Simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)].
  
  ## Expert Answers
  
  We need to simplify [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]
  
  [(x^2+3x+2)/(x-2)]*[(x^2-4)/(x-1)]
  
  use x^2 - 4 = (x - 2)(x +2), also let's find the factors of x^2+3x+2
  
  => [(x^2 + 2x + x +2)/(x-2)]*[(x - 2)(x + 2)/(x-1)]
  
  => [(x + 2)(x + 1)/(x - 2)]*[(x - 2)(x + 2)/(x-1)]
  
  cancel the common terms in the numerator and denominator
  
  => (x + 2)^2*(x + 1)/(x - 1)
  
  The simplified form of the given expression is (x + 2)^2*(x + 1)/(x - 1)
  
  Approved by eNotes Editorial Team
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question asking for the simplification of a given algebraic expression involving fractions. It also includes a detailed step-by-step solution to the problem.
  
  Label: question-and-answer