text: # How do you solve 2/(x+1) + 5/(x-2)=-2?
  
  Aug 6, 2018
  
  $x = - 3 \mathmr{and} x = \frac{1}{2}$
  
  #### Explanation:
  
  Here ,
  
  $\frac{2}{x + 1} + \frac{5}{x - 2} = - 2$
  
  Combine the fractions :
  
  $\frac{2 \left(x - 2\right) + 5 \left(x + 1\right)}{\left(x - 2\right) \left(x + 1\right)} = \frac{- 2 \left(x + 1\right) \left(x - 2\right)}{\left(x + 1\right) \left(x - 2\right)}$
  
  Simplifying we get
  
  $2 \left(x - 2\right) + 5 \left(x + 1\right) = - 2 \left(x + 1\right) \left(x - 2\right)$
  
  Using distributive property :
  
  $2 x - 4 + 5 x + 5 = - 2 \left({x}^{2} - 2 x + x - 2\right)$
  
  $\therefore 7 x + 1 = - 2 {x}^{2} + 2 x + 4$
  
  $\therefore 2 {x}^{2} + 5 x - 3 = 0$
  
  $\therefore 2 {x}^{2} + 6 x - x - 3 = 0$
  
  $\therefore 2 x \left(x + 3\right) - 1 \left(x + 3\right) = 0$
  
  $\therefore \left(x + 3\right) \left(2 x - 1\right) = 0$
  
  $\therefore x + 3 = 0 \mathmr{and} 2 x - 1 = 0$
  
  $\therefore x = - 3 \mathmr{and} x = \frac{1}{2}$
explanation: The document contains a math question and its corresponding answer. The question is about solving the equation \(\frac{2}{x+1} + \frac{5}{x-2} = -2\), and the answer provides a detailed step-by-step solution, leading to the solutions \(x = -3\) and \(x = \frac{1}{2}\).
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 2/(x+1) + 5/(x-2)=-2?
  
  Aug 6, 2018
  
  $x = - 3 \mathmr{and} x = \frac{1}{2}$
  
  #### Explanation:
  
  Here ,
  
  $\frac{2}{x + 1} + \frac{5}{x - 2} = - 2$
  
  Combine the fractions :
  
  $\frac{2 \left(x - 2\right) + 5 \left(x + 1\right)}{\left(x - 2\right) \left(x + 1\right)} = \frac{- 2 \left(x + 1\right) \left(x - 2\right)}{\left(x + 1\right) \left(x - 2\right)}$
  
  Simplifying we get
  
  $2 \left(x - 2\right) + 5 \left(x + 1\right) = - 2 \left(x + 1\right) \left(x - 2\right)$
  
  Using distributive property :
  
  $2 x - 4 + 5 x + 5 = - 2 \left({x}^{2} - 2 x + x - 2\right)$
  
  $\therefore 7 x + 1 = - 2 {x}^{2} + 2 x + 4$
  
  $\therefore 2 {x}^{2} + 5 x - 3 = 0$
  
  $\therefore 2 {x}^{2} + 6 x - x - 3 = 0$
  
  $\therefore 2 x \left(x + 3\right) - 1 \left(x + 3\right) = 0$
  
  $\therefore \left(x + 3\right) \left(2 x - 1\right) = 0$
  
  $\therefore x + 3 = 0 \mathmr{and} 2 x - 1 = 0$
  
  $\therefore x = - 3 \mathmr{and} x = \frac{1}{2}$
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 \(\frac{2}{x+1} + \frac{5}{x-2} = -2\), and the answer provides a detailed step-by-step solution, leading to the solutions \(x = -3\) and \(x = \frac{1}{2}\).
  
  Label: question-and-answer