Chapter 8
                                    Rational Expressions and 
                                                                 Functions
                             Copyright © 2010 Pearson Education, Inc.  All rights reserved                                                      Sec 8.3 - 2
                                                                         8.3
                                                Complex Fractions
                             Copyright © 2010 Pearson Education, Inc.  All rights reserved                                                      Sec 8.3 - 3
                                                      8.3 Complex Fractions
                                                                     Objectives
           1.         Simplify complex fractions by simplifying the 
                      numerator and denominator. (Method 1)
           2.         Simplify complex fractions by multiplying by a 
                      common denominator. (Method 2)
           3.         Compare the two methods of simplifying complex 
                      fractions.
           4.         Simplify rational expressions with negative 
                      exponents.
                     Copyright © 2010 Pearson Education, Inc.  All rights reserved.                                                              Sec 8.3 - 4
                                                      8.3 Complex Fractions
                                                          Complex Fractions
       A complex fraction is an expression having a fraction in the numerator,
       denominator, or both. Examples of complex fractions include
                                    2       –                                                         a2 – 16
                                    x               7                       5                           a + 2
                                            x           ,                   m ,                         a – 3             .
                                                                            n                          a2 + 4
                     Copyright © 2010 Pearson Education, Inc.  All rights reserved.                                                              Sec 8.3 - 5
                              8.3 Complex Fractions
                       Simplifying Complex Fractions
    Simplifying a Complex Fraction: Method 1
    Step 1   Simplify the numerator and denominator separately.
    Step 2   Divide by multiplying the numerator by the reciprocal of the 
              denominator.
    Step 3   Simplify the resulting fraction, if possible.
            Copyright © 2010 Pearson Education, Inc.  All rights reserved.     Sec 8.3 - 6