Multiplying and Dividing Rational Expressions - PowerPoint PPT Presentation

1 / 38
About This Presentation
Title:

Multiplying and Dividing Rational Expressions

Description:

... of polynomials, you can simplify them the same way as you simplify fractions. ... Check The calculator screens suggest that = except when x = 2. or x = 4. ... – PowerPoint PPT presentation

Number of Views:1706
Avg rating:3.0/5.0
Slides: 39
Provided by: HRW51
Category:

less

Transcript and Presenter's Notes

Title: Multiplying and Dividing Rational Expressions


1
Multiplying and Dividing Rational Expressions
8-2
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 2
2
Warm Up Simplify each expression. Assume all
variables are nonzero.
1. x5 ? x2
x7
2. y3 ? y3
y6
3.
4.
x4
Factor each expression.
5. x2 2x 8
(x 4)(x 2)
6. x2 5x
x(x 5)
7. x5 9x3
x3(x 3)(x 3)
3
Objectives
Simplify rational expressions. Multiply and
divide rational expressions.
4
Vocabulary
rational expression
5
(No Transcript)
6
Because rational expressions are ratios of
polynomials, you can simplify them the same way
as you simplify fractions. Recall that to write a
fraction in simplest form, you can divide out
common factors in the numerator and denominator.
7
Example 1A Simplifying Rational Expressions
Simplify. Identify any x-values for which the
expression is undefined.
Quotient of Powers Property
The expression is undefined at x 0 because this
value of x makes 6x4 equal 0.
8
Example 1B Simplifying Rational Expressions
Simplify. Identify any x-values for which the
expression is undefined.
Factor then divide out common factors.

The expression is undefined at x 1 and x 3
because these values of x make the factors (x
1) and (x 3) equal 0.
9
Example 1B Continued
Check Substitute x 1 and x 3 into the
original expression.


Both values of x result in division by 0, which
is undefined.
10
Check It Out! Example 1a
Simplify. Identify any x-values for which the
expression is undefined.
Quotient of Powers Property
The expression is undefined at x 0 because this
value of x makes 8x2 equal 0.
11
Check It Out! Example 1b
Simplify. Identify any x-values for which the
expression is undefined.
Factor then divide out common factors.

12
Check It Out! Example 1b Continued

Both values of x result in division by 0, which
is undefined.
13
Check It Out! Example 1c
Simplify. Identify any x-values for which the
expression is undefined.
Factor then divide out common factors.

14
Check It Out! Example 1c Continued
Both values of x result in division by 0, which
is undefined.
15
Example 2 Simplifying by Factoring by 1
Simplify . Identify any x
values for which the expression is undefined.
Factor out 1 in the numerator so that x2 is
positive, and reorder the terms.
Factor the numerator and denominator. Divide out
common factors.
Simplify.
The expression is undefined at x 2 and x 4.
16
Example 2 Continued
Check The calculator screens suggest that

except when x 2 or x 4.
17
Check It Out! Example 2a
Simplify . Identify any x
values for which the expression is undefined.
Factor out 1 in the numerator so that x is
positive, and reorder the terms.
Factor the numerator and denominator. Divide out
common factors.
Simplify.
The expression is undefined at x 5.
18
Check It Out! Example 2a Continued
Check The calculator screens suggest that
2 except when
x 5.
19
Check It Out! Example 2b
Simplify . Identify any x
values for which the expression is undefined.
Factor out 1 in the numerator so that x is
positive, and reorder the terms.
Factor the numerator and denominator. Divide out
common factors.
Simplify.
20
Check It Out! Example 2b Continued
21
You can multiply rational expressions the same
way that you multiply fractions.
22
Example 3 Multiplying Rational Expressions
Multiply. Assume that all expressions are defined.
A.
B.
3
5
3
23
Check It Out! Example 3
Multiply. Assume that all expressions are defined.
A.
B.
2
2
2
3
24
You can also divide rational expressions. Recall
that to divide by a fraction, you multiply by its
reciprocal.
2

25
Example 4A Dividing Rational Expressions
Divide. Assume that all expressions are defined.
Rewrite as multiplication by the reciprocal.
2
3
3
26
Example 4B Dividing Rational Expressions
Divide. Assume that all expressions are defined.
Rewrite as multiplication by the reciprocal.
27
Check It Out! Example 4a
Divide. Assume that all expressions are defined.
Rewrite as multiplication by the reciprocal.
3
1
x4 y
2
28
Check It Out! Example 4b
Divide. Assume that all expressions are defined.
29
Example 5A Solving Simple Rational Equations
Solve. Check your solution.
Note that x ? 5.
x 5 14
x 9
30
Example 5A Continued
Check
14
14 14
31
Example 5B Solving Simple Rational Equations
Solve. Check your solution.
Note that x ? 2.
x 5 7
x 2
Because the left side of the original equation is
undefined when x 2, there is no solution.
32
Example 5B Continued
Check A graphing calculator shows that 2 is
not a solution.
33
Check It Out! Example 5a
Solve. Check your solution.
Note that x ? 4.
x 3 7
x 4
Because the left side of the original equation is
undefined when x 4, there is no solution.
34
Check It Out! Example 5a Continued
Check A graphing calculator shows that 4 is
not a solution.
35
Check It Out! Example 5b
Solve. Check your solution.
2x 3 5
x 4
36
Check It Out! Example 5b Continued
Check
5
5 5
37
Lesson Quiz Part I
Simplify. Identify any x-values for which the
expression is undefined.
1.
x ? 2, 5
x ? 1, 6
2.
38
Lesson Quiz Part II
Multiply or divide. Assume that all expressions
are defined.
3.
4.
Solve. Check your solution.
5.
x 4
Write a Comment
User Comments (0)
About PowerShow.com