Finding the LCDFind the LCD for andStep 1 Factor each denominator.Step 2 The greatest number of times 2 appears is two, the greatest number of times 3
appears is one, and the greatest number of times rappears is three.
Step 3 LCD= 22 # 3 #r^3 = 12 r^3 NOW TRY4 r^3 = 2 # 2 #r^3 = 22 #r^3
6 r^2 = 2 # 3 #r^2
3
4 r^3.
5
6 r^2EXAMPLE 2436 CHAPTER 7 Rational Expressions and Applications
CAUTION When finding the LCD, use each factor the greatestnumber of times
it appears in any singledenominator, not the totalnumber of times it appears. For
instance, the greatest number of times rappears as a factor in one denominator in
Example 2is 3, not5.Finding LCDs
Find the LCD for the fractions in each list.(a)Factor each denominator.Use each different factor the greatest number of times it appears.LCD= 5 #m# 1 m- 32 = 5 m 1 m- 32
m^2 - 3 m =m 1 m- 325 m = 5 #m
6
5 m,
4
m^2 - 3 mEXAMPLE 3Be sure to include
mas a factor in
the LCD.Because mis not a factorof both mand must appear in the LCD.(b)Factor each denominator.Use each different factor the greatest number of times it appears as a factor.
LCD= 1 r- 5221 r+ 121 r+ 42r^2 - 10 r+ 25 = 1 r- 522r^2 - r- 20 = 1 r- 521 r+ 42r^2 - 4 r- 5 = 1 r- 521 r+ 121
r^2 - 10 r+ 253
r^2 - r- 20,
1
r^2 - 4 r- 5,
m-3, m- 3Be sure to include
the exponent 2.
(c)The expressions and are opposites of each other. This means that if
we multiply by we will getTherefore, either q- 5 or 5 - qcan be used as the LCD. NOW TRY- 1 q- 52 =-q+ 5 = 5 - q
q- 5 - 1, 5 - q.q- 5 5 - q3
5 - q1
q- 5,
NOW TRY
EXERCISE 2
Find the LCD for the pair of
fractions.
and7
8 x^35
6 x^4NOW TRY ANSWERS
- 24 x^4
NOW TRY
EXERCISE 3
Find the LCD for the fractions
in each list.
(a)
(b)
(c)
2
a- 4
,1
4 - a5
x^2 + 2 x- 82
x^2 + 6 x+ 9,1
x^2 + 7 x+ 12,t+ 4
t^2 - 253 t
2 t^2 - 10 t
,- (a)
(b)
(c)either or 4a- 4 - a
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