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9.6 Solving Rational Equations

9.6 Solving Rational Equations. p.569 What is the easiest way to solve a rational equation? What is an extraneous solution? How do you know when to cross multiply or multiply out the denominator?. Hint for solving:.

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9.6 Solving Rational Equations

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  1. 9.6 Solving Rational Equations p.569 What is the easiest way to solve a rational equation? What is an extraneous solution? How do you know when to cross multiply or multiply out the denominator?

  2. Hint for solving: • A quick way to solve a rational equation is to multiply everything through by the LCD. • This will get rid of all the fractions! • Beware of extraneous solutions!

  3. Example: Solve. LCD: 2x Multiply each fraction through by the LCD Check your solution!

  4. Solve. LCD: ? LCD: (x+1) ? Check your solution! No Solution!

  5. Solve. Factor 1st! LCD: (x+2)(x-2) Check your solutions!

  6. Short Cut! When there is only one fraction on each side of the =, just cross multiply as if you are solving a proportion.

  7. Example: Solve. Check your solutions!

  8. Last Example: Solve. Check your solutions!

  9. What is the easiest way to solve a rational equation? Multiply the equation by a value that will make the denominator equal to 1. • What is an extraneous solution? A solution that does not make a true statement in the original equation. • How do you know when to cross multiply or multiply out the denominator? Cross multiply if there is only one fraction on each side of the equal sign, otherwise multiply out the denominator.

  10. Assignment 9.6 p. 571 15-49 odd Skip 45

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