text: # Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:
  
  ## Presentation on theme: "Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:"— Presentation transcript:
  
  Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:
  
  To solve a rational equation: 1) Find the LCD of all rational expressions in the equation. 2) Multiply both sides of the equation by the LCD. 3) Solve the resulting equation.
  
  Example 1 First determine any restrictions on the variable. These are values of x for which any denominator is zero. Solve: In this case, x cannot be zero.
  
  Determine the LCD Multiply both sides of the equation by the LCD
  
  These solutions must be compared with the restriction on x found at the beginning of the problem, x ≠ 0. Since neither value is zero, we have the solution.
  
  Example 2 Determine any restrictions on the variable. Solve:
  
  Determine the LCD Multiply both sides of the equation by the LCD. This is the same as multiplying every term by the LCD.
  
  Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 4,2. Since the solution does not match either restriction, we have the solution.
  
  Example 3 Determine any restrictions on the variable. Solve:
  
  Determine the LCD Multiply every term by the LCD.
  
  Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 5,0. Since in this case the result is one of the restricted values, it cannot be a solution to the equation. The answer is written as …
  
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explanation: The document is a presentation transcript or outline on solving rational equations. It defines rational equations, provides steps for solving them, and includes three examples with solutions. The text contains multiple questions and answers within the examples.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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distilabel_metadata.content: # Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:
  
  ## Presentation on theme: "Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:"— Presentation transcript:
  
  Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:
  
  To solve a rational equation: 1) Find the LCD of all rational expressions in the equation. 2) Multiply both sides of the equation by the LCD. 3) Solve the resulting equation.
  
  Example 1 First determine any restrictions on the variable. These are values of x for which any denominator is zero. Solve: In this case, x cannot be zero.
  
  Determine the LCD Multiply both sides of the equation by the LCD
  
  These solutions must be compared with the restriction on x found at the beginning of the problem, x ≠ 0. Since neither value is zero, we have the solution.
  
  Example 2 Determine any restrictions on the variable. Solve:
  
  Determine the LCD Multiply both sides of the equation by the LCD. This is the same as multiplying every term by the LCD.
  
  Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 4,2. Since the solution does not match either restriction, we have the solution.
  
  Example 3 Determine any restrictions on the variable. Solve:
  
  Determine the LCD Multiply every term by the LCD.
  
  Compare this solution with the restrictions on x found at the beginning of the problem, x ≠ - 5,0. Since in this case the result is one of the restricted values, it cannot be a solution to the equation. The answer is written as …
  
  Download ppt "Solving Rational Equations A Rational Equation is an equation that contains one or more rational expressions. The following are rational equations:"
  
  Similar presentations
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a presentation transcript or outline on solving rational equations. It defines rational equations, provides steps for solving them, and includes three examples with solutions. The text contains multiple questions and answers within the examples.
  
  Label: multiple-question-and-answer