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9.6 Solving Rational Equations and Inequalities

9.6 Solving Rational Equations and Inequalities. Extraneous Solutions. An extraneous solution can be introduced when multiplying both sides of an equation by the same algebraic expression. An extraneous solution is a solution of the derived equation but not the original.

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9.6 Solving Rational Equations and Inequalities

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  1. 9.6Solving Rational Equations and Inequalities

  2. Extraneous Solutions • An extraneous solution can be introduced when multiplying both sides of an equation by the same algebraic expression. • An extraneous solution is a solution of the derived equation but not the original. • CHECK for extraneous solutions.

  3. Ex 1

  4. Ex 2

  5. Ex 3

  6. Ex 4

  7. Ex 5 Rose can jog 5 mi downhill in the same time it takes her to jog 3 mi uphill. She jogs downhill 4mi/h faster than she jogs uphill. Find her jogging rate each way.

  8. Ex 6 Jim & Al have to paint 6000 square feet of hallway in an office building. Al works twice as fast as Jim. Working together, they can complete the job in 15 hours. How long would it take each of them working alone?

  9. Ex 7 George can mow his lawn in 4 hours. Kate can do the job in 3 hours. How long will it take them to do the job together?

  10. Rational Inequalities • State the excluded values. • Solve the related equation. • Use the values from steps 1 & 2 to divide a number line into regions. Test the values in each region to see which satisfy the original inequality.

  11. Ex 8

  12. Ex 9

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