Carson Elementary And Intermediate Algebra 3e

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Carson Elementary and Intermediate Algebra 3e
Section 7.4.1-2
Objectives
1.
Find the LCD of two or more rational expressions.
Vocabulary
Prior Knowledge
Finding LCD for arithmetic fractions.
New Concepts
Skip 7.4.2-3 (Add and subtract rational expressions with different denominators.)
1. Find LCD of two or more rational expressions.
Our goal is to solve rational equations. Let’s go back to the earlier equations we solved in Chapter 2 that
contained fractions.
7
x
5
x
1
12
8
4
To solve this, the first step is to clear the fractions by multiplying each term by the least common
denominator, which, in this case, is 24.
Where did the 24 come from? We’ve been finding LCDs for so long that at this point we may have forgotten
how we originally found them. When you first learned to find LCDs, the first step was to factor each
denominator into prime factors.
12
8
4
2 · 2 · 3
2 · 2 · 2
2 · 2
The least common denominator is found by writing
all of the factors for the first
number, followed by
any that
are not already included
from the other denominators.
12
8
4
2 · 2 · 3
2 · 2 · 2
2 · 2
LCD = 2 · 2 · 3 ·
2
= 24
LCD = 2 · 2 · 3 · 2 = 24
5
3
Example 1:
Find the LCD for
and
.
6
10
We know it is 30 but where did it come from?
Factor each denominator.
6
10
2 · 3
2 · 5
LCD = 2 · 3 · 5 = 30
Write ALL of the factors for the first number and then any
additional factors from the second number.
V. Zabrocki 2011
page 1

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