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RATIONAL EXPRESSIONS




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Educational Resources       this www.podiumfiles.com
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Rational Expression
                                                     Objective

To be able to simplify a rational expression

 PRIME!                     numerator
                5
              x + 2
                            denominator



                                                  at
    Educational Resources                     this www.podiumfiles.com
                                          Get
Rational Expressions
                            Simplifying rational expressions


       - Factor the numerator.
       - Factor the denominator.
       - Divide out the common factors.
       - Write in simplified form.




                                                  at
    Educational Resources                     this www.podiumfiles.com
                                          Get
Rational Expressions
                                  Simplifying rational expressions
      2
 3x     + 9x               Step 1: Look for common factors
          3                to both terms in the numerator.
      12x
                           - 3 is a factor of both 3 and 9.
                           - x is a factor of both x2 and x.


                                  Step 2: Factor the numerator


                                                          at
          Educational Resources                       this www.podiumfiles.com
                                                  Get
Rational Expressions
                                  Simplifying rational expressions
      2
 3x     + 9x                       Step 3: Look for common factors in
                                   the denominator
          3
      12x                          There’s only one term in the
                                   denominator but it can still be
                                   factored out.




                                                            at
          Educational Resources                         this www.podiumfiles.com
                                                    Get
Rational Expressions
                                  Simplifying rational expressions
      2
 3x     + 9x
          3                        Step 4: Divide and simplify
      12x


                                                                 x +3
                                                                      2
                                                                 4x
                                                         at
          Educational Resources                      this www.podiumfiles.com
                                                 Get
Rational Expressions
                                           Exercises



                        2
                 9 x yz
    1.                      2
                24 xyz


                                        at
    Educational Resources           this www.podiumfiles.com
                                Get
Rational Expressions
                                              Exercises



                 9 x yz 2         3x
    1.                      2
                                =
                24 xyz            8z


                                           at
    Educational Resources              this www.podiumfiles.com
                                   Get
Rational Expressions
                                            Exercises



                      a + 3
     2.           2
              a       + 4a + 3




                                         at
    Educational Resources            this www.podiumfiles.com
                                 Get
Rational Expressions
                                               Exercises



                      a + 3          1
     2.           2
                      + 4a + 3
                                 =
              a                    a +1


                                            at
    Educational Resources               this www.podiumfiles.com
                                    Get
Rational Expressions
                                            Exercises



                     3x − 15
       3.        2
             x       − 7x + 10




                                         at
    Educational Resources            this www.podiumfiles.com
                                 Get
Rational Expressions
                                                  Exercises



                     3x − 15           3
       3.        2
                     − 7x + 10
                                 =
             x                       x − 2



                                               at
    Educational Resources                  this www.podiumfiles.com
                                       Get

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Rational Expressions

  • 1. RATIONAL EXPRESSIONS at Educational Resources this www.podiumfiles.com Get
  • 2. Rational Expression Objective To be able to simplify a rational expression PRIME! numerator 5 x + 2 denominator at Educational Resources this www.podiumfiles.com Get
  • 3. Rational Expressions Simplifying rational expressions - Factor the numerator. - Factor the denominator. - Divide out the common factors. - Write in simplified form. at Educational Resources this www.podiumfiles.com Get
  • 4. Rational Expressions Simplifying rational expressions 2 3x + 9x Step 1: Look for common factors 3 to both terms in the numerator. 12x - 3 is a factor of both 3 and 9. - x is a factor of both x2 and x. Step 2: Factor the numerator at Educational Resources this www.podiumfiles.com Get
  • 5. Rational Expressions Simplifying rational expressions 2 3x + 9x Step 3: Look for common factors in the denominator 3 12x There’s only one term in the denominator but it can still be factored out. at Educational Resources this www.podiumfiles.com Get
  • 6. Rational Expressions Simplifying rational expressions 2 3x + 9x 3 Step 4: Divide and simplify 12x x +3 2 4x at Educational Resources this www.podiumfiles.com Get
  • 7. Rational Expressions Exercises 2 9 x yz 1. 2 24 xyz at Educational Resources this www.podiumfiles.com Get
  • 8. Rational Expressions Exercises 9 x yz 2 3x 1. 2 = 24 xyz 8z at Educational Resources this www.podiumfiles.com Get
  • 9. Rational Expressions Exercises a + 3 2. 2 a + 4a + 3 at Educational Resources this www.podiumfiles.com Get
  • 10. Rational Expressions Exercises a + 3 1 2. 2 + 4a + 3 = a a +1 at Educational Resources this www.podiumfiles.com Get
  • 11. Rational Expressions Exercises 3x − 15 3. 2 x − 7x + 10 at Educational Resources this www.podiumfiles.com Get
  • 12. Rational Expressions Exercises 3x − 15 3 3. 2 − 7x + 10 = x x − 2 at Educational Resources this www.podiumfiles.com Get