Chapter 8
                                    Rational Expressions and 
                                                                 Functions
                             Copyright © 2010 Pearson Education, Inc.  All rights reserved                                                      Sec 8.2 - 2
                                                                         8.2
                                       Adding and Subtracting 
                                            Rational Expressions
                             Copyright © 2010 Pearson Education, Inc.  All rights reserved                                                      Sec 8.2 - 3
                   8.2 Adding and Subtracting Rational Expressions
                                                                     Objectives
           1.         Add and subtract rational expressions with the 
                      same denominator.
           2.         Find a least common denominator.
           3.         Add and subtract rational expressions with 
                      different denominators.
                     Copyright © 2010 Pearson Education, Inc.  All rights reserved.                                                              Sec 8.2 - 4
                   8.2 Adding and Subtracting Rational Expressions
                                                       Rational Expressions
       Adding or Subtracting Rational Expressions
       Step 1   If the denominators are the same, add or subtract the numerators.
                       Place the result over the common denominator.
                       If the denominators are different, first find the least common 
                       denominator. Write all rational expressions with this LCD, and then
                        add or subtract the numerators. Place the result over the common
                        denominator.
       Step 2   Simplify. Write all answers in lowest terms.
                     Copyright © 2010 Pearson Education, Inc.  All rights reserved.                                                              Sec 8.2 - 5
          8.2 Adding and Subtracting Rational Expressions
     EXAMPLE 1         Adding and Subtracting Rational Expressions
                                   with the Same Denominator
  Add or subtract as indicated.
   (a)    4m + 5n        =    4m  +  5n          Add the numerators.
           7        7             7              Keep the common denominator.
   (b)     1    –   5    =     1  –  5           Subtract the numerators; keep the
           g3      g3            g3              common denominator.
                          =     – 4
                                    3              Simplify.
                                   g
            Copyright © 2010 Pearson Education, Inc.  All rights reserved.   Sec 8.2 - 6