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Section 7-10: Fractional Equations and Extraneous Solutions

CHAPTER SEVEN: RATIONAL ALGEBRAIC FUNCTIONS. Section 7-10: Fractional Equations and Extraneous Solutions . Objective:. Given a fractional equation, be able to solve it. Fractional Equation. A fractional equation is an equation that has a variable in a denominator. For example:.

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Section 7-10: Fractional Equations and Extraneous Solutions

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  1. CHAPTER SEVEN: RATIONAL ALGEBRAIC FUNCTIONS Section 7-10: Fractional Equations and Extraneous Solutions

  2. Objective: • Given a fractional equation, be able to solve it.

  3. Fractional Equation • A fractional equation is an equation that has a variable in a denominator. • For example: We need to find the LCM of the denominators to solve.

  4. Solving a Fractional Equation

  5. Extraneous Solution • In the example, we got the following two solutions: • x = -7 • x = 2 • Before writing the solution set, you must look back at the excluded values. Because 2 is one of our excluded values, it is said to be an extraneous solution.

  6. Example • Solve the equation and write the solution set.

  7. Example • Solve the equation and write the solution set.

  8. Technique for Solving Fractional Equations • Write the domain. • Multiply both members of the equation by the smallest expression needed to eliminate all of the fractions. • Solve the resulting polynomial equation. • Discard any extraneous solutions. • Write the solution set.

  9. HOMEWORK: PAGE 381 # 21-41 odd

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