Download Section 7.4

Chapter 7
Section 4
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
7.4
1
Equations with Rational Expressions
and Graphs
Solve rational equations.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
A rational equation is an equation that contains at
least one rational expression with a variable in the
denominator.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 3
The easiest way to solve most rational equations is to
multiply all terms in the equation by the least common
denominator.
This step will clear the equation of all denominators. It
is necessary to either check the proposed solutions or
verify that they are in the domain.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 4
CAUTION When both sides of an equation are
multiplied by a variable expression, the resulting
proposed solutions may not satisfy the original
equation.
You must either determine and observe the
domain or check all proposed solutions in the
original equation. It is wise to do both.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 5
EXAMPLE 1
Solve.
3 2 5
  
20 x 4 x
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 6
EXAMPLE 2
Solve.
3
1
2

 2
x 1 x 1 x 1
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 7
EXAMPLE 3
Solve.
4
1
2
 2
 2
2
x  x  6 x  4 x  5x  6
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 8
EXAMPLE 4
Solve.
2
1
 x  3x

 2
x  3 x 1 x  2x  3
2
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Slide 7.4- 9
EXAMPLE 5
Solve.
4
x   5
x
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 10
EXAMPLE 6
Solve.
y2
6


0
2
2
y  y y 1
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7.4- 11