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Concept 5

Concept 5. Rational expressions. Rational Expressions. 2. Rational Expression - the ratio of _____ polynomials. (Like a _____________ with a polynomial in the ________________ and the ______________________. Examples : Non-Examples : Characteristics : 1 . 2.

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Concept 5

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  1. Concept 5 Rational expressions

  2. Rational Expressions 2 • Rational Expression - the ratio of _____ polynomials. (Like a _____________ with a polynomial in the ________________ and the ______________________. • Examples: Non-Examples: • Characteristics: 1. 2. numerator fraction denominator

  3. Factor top & bottom: Cancel & Reduce if possible:

  4. Factor top & bottom: Cancel & Reduce if possible:

  5. Examples: 1. 2. 3. 4.

  6. 5. 6. 7. 8. 9.

  7. Solving Polynomials Concept 6

  8. To solve a polynomial, factor completely. Any terms can then be set equal to zero and solve for x. 5 5

  9. 7 7

  10. Quadratic Formula – used to solve equations when it can’t be factored. • Before substituting in values for a, b, and c, rearrange the equation to look like. The quadratic formula is used to solve for values that make the equation true and are not factorable.

  11. So a = = 1 b = = -8 c = = -48 -48 1 -8 -8 1

  12. So a = = 6 b = = 9 c = = -18

  13. Concept 7: evaluating and finding zeros of rational expressions.

  14. Evaluating Rational Expressions • Evaluating—Substituting a specific value in for x into a rational expressions and evaluating to find a specific answer. Evaluate when x = 1

  15. undefined

  16. Evaluate at the given values of x. a. x = 1 b. x = -5 c. x = 4

  17. Finding zeros— finding the values of the variable that makes the denominator of a rational expression zero. Find the values that make the denominator zero.

  18. Finding zeros— finding the values of the variable that makes the denominator of a rational expression zero.

  19. Concept 8: Multiplying Rational Expressions

  20. Multiplying Rational Numbers Step 1: Factor both the _________________ and the _______________ Step 2: Write together as one fraction, by ____________ _______. Step 3 : ___________ the expression. Step 4: Multiply _________ remaining factors in the _______________ or the ____________________. numerator denominator multiplying across Simplify any numerator denominator

  21. 1 1. 2 2.

  22. 2 2(x – 6) 3. 1 3(x – 6) 4.

  23. (x - 2)(x + 5) 2 5. 1 5(x + 9) x 6. (x + 9)(x - 9)

  24. (x + 2)(x - 6) 7. (x - 2)(x + 2) (x - 3)(x - 6) 2( 2( ( 8. (

  25. (x - 7)(x + 7) (x - 7)(x - 3) 9. (x - 3)(x + 3) x(x +4)(x + 7)

  26. (x + 11)(x + 11) 10. 4 2x(x - 2) 5x (x + 7)(x - 7) 11. 1 2 2

  27. Concept 9: Dividing Rational Expressions multiply do not We ___________ divide rational expressions we ______________ by the ________________ of the ___________ expression. reciprocal last

  28. 1 1. 1 1 1 1 2. x 1 1

  29. 3. 1 1 1 5 4.

  30. 5. 6.

  31. 7. 8.

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