Rational expressions and equations

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  • 1. Rational Expressions and Equations Chapter 9 pg 470
  • 2. Review of Rational Expressions
    • A rational expression is an expression that is the quotient of two polynomials.
    • Examples include
  • 3. Domain of a Rational Expression
    • The domain of a rational expression is the set of real numbers for which the expression is defined.
    • The domain consists of all real numbers except those that make the denominator 0.
  • 4. Domain of a Rational Expression
    • For example, to find the domain of
    • solve as follows,
    • or
    • or
    • The domain is
  • 5. Lowest Terms of a Rational Expression Fundamental Principle of Fractions
  • 6. Writing Rational Expressions in Lowest Terms
    • Example Write each rational expression in lowest terms.
    • (a) (b)
    • Solution
    • (a)
    • by the fundamental principle, provided p is not 0 or –4.
  • 7. Writing Rational Expressions in Lowest Terms
    • Solution
    • (b)
    • by the fundamental principle.
  • 8. Multiplying and Dividing Rational Expressions Multiplying and Dividing Fractions For fractions and and
  • 9. Multiplying and Dividing Rational Expressions
    • Example Multiply or divide as indicated.
    • (a) (b)
    • Solution
    • (a)
  • 10. Multiplying and Dividing Rational Expressions
    • Solution (b)
  • 11. Complex Fractions
    • Complex fractions are those fractions whose numerator & denominator both contain fractions.
  • 12. Now you try!
    • Pg 476- 477
    • #’s 14-22 evens
    • #’s 26-34 evens
    • #’s 36, 37, 38
  • 13. Adding and Subtracting Rational Expressions Adding and Subtracting Fractions For fractions and and
    • Addition and subtraction are typically performed using the
    • least common denominator.
  • 14. Adding and Subtracting Rational Expressions
    • Finding the Least Common Denominator (LCD)
    • Write each denominator as a product of prime factors.
    • Form a product of all the different prime factors. Each factor should have as exponent the greatest exponent that appears on that factor.
  • 15. Adding/Subtracting
    • when we talk about CDs, we mean denominators that contain the same factors.
    • To find our CD, we will first factor the ones we have.
    • Then we will multiply each denominator by the factors it is missing to create a CD.
    • Remember, we must also multiply the numerator by that same factor.
  • 16. Adding and Subtracting Rational Expressions
    • Example Add or subtract, as indicated.
    • (a) (b)
    • Solution
    • (a) Step 1: Find the LCD
  • 17. Adding and Subtracting Rational Expressions
    • Solution (a) The LCD is
    • Then
  • 18. Adding and Subtracting Rational Expressions
    • Solution (b)
  • 19. Now you try!
    • Pg 482- 483 #’s 26-36 evens
  • 20. Complex Fractions
    • A complex fraction is any quotient of two rational expressions.
  • 21. Simplifying Complex Fractions
    • Example Simplify
    • Solution
    • Multiply both numerator and denominator by the LCD
    • of all the fractions a ( a + 1).
  • 22. Simplifying Complex Fractions
    • Solution
  • 23. Now you try!
    • Pg 483 #’s 40