text: # publicKhan/khan-exercises
  
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  file 102 lines (93 sloc) 5.472 kb
   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 `        Simplifying rational expressions 3
  
  randVar()                    randVar()                    randRangeNonZero(-10, 10)
  randRangeWeighted(-10, 10, 0, 0.5)                        randRangeWeighted(-10, 10, 0, 0.5)
  new RationalExpression([[1, X], A])                    new RationalExpression([[1, X], B])                    new RationalExpression([[1, X], C])                    FACTOR1.multiply(FACTOR2)                    FACTOR1.multiply(FACTOR3)
  
  Simplify the following expression and state the condition under which the simplification is valid:
  
  Y = \dfrac{NUMERATOR}{DENOMINATOR}
  
  FACTOR2.regex()                        FACTOR3.regex()                        -A
  
  FACTOR2.multiply(-1).regex()                        FACTOR3.multiply(-1).regex()                        -A
  
  Y =
  a
  a
  \space X \neq a
  
  a simplifed expression, like x + 2
  
  First factor the expressions in the numerator and denominator.
  
  \dfrac{NUMERATOR}{DENOMINATOR}                        = \dfrac{(FACTOR2)(FACTOR1)}{(FACTOR3)(FACTOR1)}
  
  Notice that the term (FACTOR1) appears in both the numerator and denominator.
  
  Dividing both the numerator and denominator by (FACTOR1) gives:
  
  Y = \dfrac{FACTOR2}{FACTOR3} or more simply,                             Y = FACTOR2
  
  Y = \dfrac{FACTOR2}{FACTOR3}
  
  Since we divided by (FACTOR1), X \neq -A.
  
  Y = writeExpressionFraction(FACTOR2, FACTOR3); \space X \neq -A
  
  `
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explanation: The document appears to be a code snippet for generating a math problem and its solution, specifically for simplifying rational expressions. It contains a question and a detailed step-by-step 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: # publicKhan/khan-exercises
  
  ### Subversion checkout URL
  
  You can clone with HTTPS or Subversion.
  
  Fetching contributors…
  
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  file 102 lines (93 sloc) 5.472 kb
   1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 `        Simplifying rational expressions 3
  
  randVar()                    randVar()                    randRangeNonZero(-10, 10)
  randRangeWeighted(-10, 10, 0, 0.5)                        randRangeWeighted(-10, 10, 0, 0.5)
  new RationalExpression([[1, X], A])                    new RationalExpression([[1, X], B])                    new RationalExpression([[1, X], C])                    FACTOR1.multiply(FACTOR2)                    FACTOR1.multiply(FACTOR3)
  
  Simplify the following expression and state the condition under which the simplification is valid:
  
  Y = \dfrac{NUMERATOR}{DENOMINATOR}
  
  FACTOR2.regex()                        FACTOR3.regex()                        -A
  
  FACTOR2.multiply(-1).regex()                        FACTOR3.multiply(-1).regex()                        -A
  
  Y =
  a
  a
  \space X \neq a
  
  a simplifed expression, like x + 2
  
  First factor the expressions in the numerator and denominator.
  
  \dfrac{NUMERATOR}{DENOMINATOR}                        = \dfrac{(FACTOR2)(FACTOR1)}{(FACTOR3)(FACTOR1)}
  
  Notice that the term (FACTOR1) appears in both the numerator and denominator.
  
  Dividing both the numerator and denominator by (FACTOR1) gives:
  
  Y = \dfrac{FACTOR2}{FACTOR3} or more simply,                             Y = FACTOR2
  
  Y = \dfrac{FACTOR2}{FACTOR3}
  
  Since we divided by (FACTOR1), X \neq -A.
  
  Y = writeExpressionFraction(FACTOR2, FACTOR3); \space X \neq -A
  
  `
  Something went wrong with that request. Please try again.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document appears to be a code snippet for generating a math problem and its solution, specifically for simplifying rational expressions. It contains a question and a detailed step-by-step answer.
  
  Label: question-and-answer