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Section 6.1

Section 6.1. Rational Expressions. Determine the values that make a rational expression undefined. A. OBJECTIVES. Build fractions. Reduce (simplify) a rational expression to lowest terms. B. C. OBJECTIVES. RULES. Avoiding Zero Denominators.

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Section 6.1

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  1. Section 6.1 Rational Expressions

  2. Determine the values that make a rational expression undefined. A OBJECTIVES

  3. Build fractions. Reduce (simplify) a rational expression to lowest terms. B C OBJECTIVES

  4. RULES Avoiding Zero Denominators The variables in a rational expression must not be replaced by numbers that make the denominator zero.

  5. RULES Fundamental Rule of Rational Expressions

  6. PROCEDURE Reducing Rational Expressions to Lowest Terms Write the numerator and denominator of the expression in factored form.

  7. PROCEDURE Reducing Rational Expressions to Lowest Terms Find the factors that are common to the numerator and denominator.

  8. Replace the quotient of the common factors by the number 1 since PROCEDURE Reducing Rational Expressions to Lowest Terms

  9. PROCEDURE Reducing Rational Expressions to Lowest Terms Rewrite the expression in simplified form.

  10. RULE Quotient of Additive Inverses

  11. Chapter 6 Rational Expressions Section 6.1Exercise #1

  12. Chapter 6 Rational Expressions Section 6.1Exercise #2

  13. Chapter 6 Rational Expressions Section 6.1Exercise #3

  14. Section 6.2 Rational Expressions

  15. Multiply two rational expressions. Divide one rational expression by another. A B OBJECTIVES

  16. RULE Multiplying Rational Expressions

  17. PROCEDURE Multiplying Rational Expressions Reduce each expression if possible. Multiply the numerators to obtain the new numerator.

  18. PROCEDURE Multiplying Rational Expressions Multiply denominators to obtain new denominator. Reduce if possible.

  19. RULE Dividing Rational Expressions

  20. Chapter 6 Rational Expressions Section 6.2Exercise #6

  21. Chapter 6 Rational Expressions Section 6.2Exercise #8

  22. Section 6.3 Rational Expressions

  23. Add and subtract rational expressions with the same denominator. A OBJECTIVES

  24. Add and subtract rational expressions with different denominators. Solve an application. B C OBJECTIVES

  25. PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Find the LCD.

  26. PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Write all fractions as equivalent ones with LCD as the denominator.

  27. PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Add or subtract numerators, keep denominators.

  28. PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Reduce if possible.

  29. Chapter 6 Rational Expressions Section 6.3Exercise #11

  30. Chapter 6 Rational Expressions Section 6.3Exercise #12

  31. Section 6.4 Rational Expressions

  32. Simplify a complex fraction using one of two methods. A OBJECTIVE

  33. DEFINITION Complex Fraction A fraction with one or more fractions in its numerator, denominator or both.

  34. PROCEDURE Simplifying Complex Fractions Multiply numerator and denominator by the LCD of the fractions involved, or

  35. PROCEDURE Simplifying Complex Fractions Perform operations indicated in numerator and denominator, then divide simplified numerator by simplified denominator.

  36. Chapter 6 Rational Expressions Section 6.4Exercise #13

  37. Section 6.5 Rational Expressions

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