chapter 6 section 5 objectives 1 copyright © 2012, 2008, 2004 pearson education, inc. complex...
TRANSCRIPT
Objectives
1
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Complex Fractions
Simplify a complex fraction by multiplying numerator and denominator by the least common denominator (Method 2).
Simplify rational expressions with negative exponents.
6.5
2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Complex Fractions.
The quotient of two mixed numbers can be written as a fraction.
Complex FractionA fraction with fractions in the numerator and/or denominator is called a complex fraction.
1 12 3
2 4
1 12 2
2 2 1 1
3 34 4
12
21
34
Numerator of complex fractionMain fraction barDenominator of complex fraction
Slide 6.5-3
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objective 1
Simplify a complex fraction by multiplying numerator and denominator by the least common denominator. (Method 2 in our Text)
Slide 6.5-9
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solution:
2 13 44 19 2
Simplify each complex fraction.
2 1
3 44 1
9
36
236
24 9
16 18
15
34
62
43
a
a
a
a
2 6
3 4
a
a
62
43
a
a
Slide 6.5-11
Simplifying Complex Fractions (Method 2)CLASSROOM EXAMPLE 4
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
This technique utilizes the Fundamental Law of Fractions.
Method 2 from our Text
Simplifying a Complex Fraction
Step 1: Find the LCD of all fractions within the complex fraction.
Step 2: Multiply both the numerator and denominator of the complex fraction by this LCD using the distributive property as necessary. Write in lowest terms.
Slide 6.5-10
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify the complex fraction.
2 2
2 2
2 3
4 1a b ab
a b ab
Solution:
2 2
22
2
2 2
2
2 3
4 1
a b ab
aa
bb
b
a
a
b
2 3
4
b a
ab
Slide 6.5-12
Simplifying a Complex Fraction (Method 2)CLASSROOM EXAMPLE 5
LCD = a2b2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Solution:1 2
1 22 1
2 3
a b
b a
Simplify the complex fraction.
2 3
1 2 8
a b a
a a b
Slide 6.5-8
Simplifying a Complex Fraction CLASSROOM EXAMPLE 3
LCD = (a+1)(b-2)(a+3)
1 2
1 22 1
2 3
a b
b a
(a+1)(b-2)(a+3)
(a+1)(b-2)(a+3)
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify each complex fraction.
1 21
41
x x
x
2
2
2 34
4 916
xxxx
2 34
2 3 2 3
4
44
4
44
x x
x x
xx
x x
x x
4
2 3
2 3
2 3
x
x
x
x
4
2 3
x
x
1 2 1
11
14
x xx
x
x
x x
1 2
4
x x
x
3 1
4
x
x
Slide 6.5-13
Deciding on a Method and Simplifying Complex Fractions
Solution:
CLASSROOM EXAMPLE 6
Note: One term distribute once, two terms distribute twice
Ex 1
Ex 2
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Simplify rational expressions with negative exponents.
Objective 2
Slide 6.5-10
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
2 1
1 35
a b
a b
Simplify the expression, using only positive exponents in the answer.
2
3
1 1
1 5a b
a b
LCD = a2b3
22
33
3
2
1 1
1 5
a
a
bb
b
a
ba
2 3 2 3
2 3 2 3
2
3
1 1
1 5a b
a b
a b a b
a b a b
3 2 2
3 25
b a b
ab a
Slide 6.5-11
CLASSROOM EXAMPLE 7
Simplifying Rational Expressions with Negative Exponents
Solution:
Negative exponent means take the reciprocal of the base.