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11.7 Solving Rational Equations

Learn how to solve rational equations efficiently by mastering cross-products, avoiding extraneous solutions, and applying step-by-step methods with examples.

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11.7 Solving Rational Equations

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  1. 11.7 Solving Rational Equations

  2. Rational Equation An equation containing one or more rational expressions

  3. Cross productsShort cut: extraneous solution?

  4. Cross products:

  5. Cross products:

  6. Cross products:

  7. Steps to solve Rational Equations • Find the LCD • Multiply every term on both sides of the equation by the LCD over 1 • Cross Cancel • Solve for the variable a. Linear equation: get variables on one side and constants on the other b. Quadratic: set your equation = 0 and factor.

  8. Extraneous Solutions • When both sides of the equation are mult by a variable, the equation is transformed into a new equation and may have an extra solution. • Check each solution in the original rational equation • Make sure that your answer does not make the denominator 0

  9. Solve for x: LCM =

  10. 2x• •2x Solve for x: LCM = 2x

  11. Solve for x: x• • x

  12. Solve for x: -2 is an extraneous solution.

  13. Assignment:Page 592 (5-10, 13-18) all

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