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Section 6.1

Section 6.1. Rational Expressions. Find the numbers that make a rational expression undefined. A. OBJECTIVES. Write an equivalent fraction with the indicated denominator. B. OBJECTIVES. Write a fraction in the standard forms. C. OBJECTIVES. Reduce a fraction to lowest terms. D.

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Section 6.1

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  1. Section 6.1 Rational Expressions

  2. Find the numbers that make a rational expression undefined. A OBJECTIVES

  3. Write an equivalent fraction with the indicated denominator. B OBJECTIVES

  4. Write a fraction in the standard forms. C OBJECTIVES

  5. Reduce a fraction to lowest terms. D OBJECTIVES

  6. DEFINITION Rational Expressions If P and Q are polynomials:

  7. DEFINITION Undefined Rational Expressions The variables in a rational expression may not be replaced by values that will make the denominator zero.

  8. DEFINITION Fundamental Property of Fractions If P, Q, and K are polynomials

  9. PROCEDURE Reducing Fractions Write numerator and denominator in factored form. Find the GCF.

  10. PROCEDURE Reducing Fractions Replace the quotient of the common factors by 1. Rewrite in lowest terms.

  11. DEFINITION Quotient of Additive Inverses

  12. Practice Test Chapter 6Section 6.1A,B Exercise #1

  13. Find the undefined value(s) for

  14. Write the fraction with the indicated denominator.

  15. Practice Test Chapter 6Section 6.1C Exercise #2

  16. Write in standard form

  17. Write in standard form

  18. Practice Test Chapter 6Section 6.1D Exercise #4

  19. Reduce to lowest terms. Factor out – 1 Difference of Squares Difference of Cubes

  20. Reduce to lowest terms.

  21. Section 6.2 Multiplication and Division of Rational Expressions

  22. Multiply rational expressions. A OBJECTIVES

  23. Divide rational expressions. B OBJECTIVES

  24. Use multiplication and division together. C OBJECTIVES

  25. DEFINITION Multiplication of Rational Expressions

  26. PROCEDURE To Multiply Rational Expressions Factor the numerators and denominators completely. Simplify each expression.

  27. PROCEDURE To Multiply Rational Expressions Multiply remaining factors. The final product should be in lowest terms.

  28. DEFINITION Division of Real Numbers

  29. Practice Test Chapter 6Section 6.2B Exercise #6

  30. Perform the indicated operations.

  31. Perform the indicated operations.

  32. Practice Test Chapter 6Section 6.2C Exercise #7

  33. Perform the indicated operations.

  34. Perform the indicated operations.

  35. Section 6.3 Addition and Subtraction of Rational Expressions

  36. Add or subtract rational expressions with the same denominator. A OBJECTIVES

  37. Add or subtract rational expressions with different denominators. B OBJECTIVES

  38. PROCEDURE Finding the LCD of Two or More Rational Expressions Factor denominators. Place factors in columns. (Not necessary to factor monomials).

  39. PROCEDURE Finding the LCD of Two or More Rational Expressions Select the factor with the greatest exponent from each column.

  40. PROCEDURE Finding the LCD of Two or More Rational Expressions The product of all the factors obtained is the LCD.

  41. PROCEDURE To Add or Subtract Fractions with Different Denominators. Find the LCD. Write all fractions as equivalent ones with LCD as denominator.

  42. PROCEDURE To Add or Subtract Fractions with Different Denominators. Add numerators. Simplify.

  43. Practice Test Chapter 6Section 6.3B Exercise #9a

  44. Perform the indicated operations.

  45. Perform the indicated operations.

  46. Perform the indicated operations.

  47. Perform the indicated operations.

  48. Section 6.4 Complex Fractions

  49. Write a complex fraction as a simple fraction in reduced form. A OBJECTIVES

  50. PROCEDURE Simplifying Complex Fractions METHOD 1 Multiply the numerator and denominator of the complex fraction by the LCD of all simple fractions.

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