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4 2x 4 2x 2 x 3x 4 x 1 x 4 x 1 x 1 x 1
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From the rst fraction we see that the LCD needs x 4 and x 1 as factors From the second fraction we see that the LCD needs x 1 and x 1, but x 1 has been accounted for by the rst fraction The LCD is x 4 x 1 x 1
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CHAPTER 6 Factoring
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Find the LCD 1: 2: 3: 4: 5: x 10 5 2 x 8x 7 2x 2
3x 22 x 14 2 x 5x 24 x x 6
7 1 x 3 3 x x 1 4 2 6x 21x 12 9x 27x 18
3 7 1 2 4x 48 6x 24 4x 20x 24
6: 7: 2x 4 x 2 x 7x 12 x 6x 9
CHAPTER 6 Factoring
6x 7 3 x2 5
Solutions
1: x 10 5 x 10 5 2 x 8x 7 2x 2 x 7 x 1 2 x 1 x 1
LCD 2 x 7 x 1 x 1 2: 3x 22 x 14 3x 22 x 14 2 x 5x 24 x x 6 x 8 x 3 x 3 x 2
LCD x 8 x 3 x 2 3: 7 1 7 1 7 1 x 3 3 x x 3 x 3 x 3 x 3
LCD x 3 4: x 1 4 x 1 2 6x 21x 12 9x 27x 18 3 2x 1 x 4 4 9 x 1 x 2
LCD 9 2x 1 x 4 x 1 x 2 5: 2x2 3 7 1 2 2 4x 48 6x 24 4x 20x 24 2 x 4 x 6 7 1 6 x 4 4 x 6 x 1
LCD 12 x 4 x 6 x 1 6: 2x 4 x 2x 4 x x2 7x 12 x2 6x 9 x 3 x 4 x 3 x 3
LCD x 3 x 3 x 4 x 3 2 x 4
CHAPTER 6 Factoring
7: 6x 7 6x 7 3 3 2 2 x 5 x 5 1
LCD x2 5 Once the LCD is found rewrite each fraction in terms of the LCD multiply each fraction by the missing factors over themselves Then add or subtract the numerators
Examples
1 x 1 x 2 x 2x 3 x 9 x 3 x 1 x 3 x 3
LCD x 3 x 1 x 3 The factor x 3 is missing in the rst denominator so multiply the x 3 An x 1 is missing from the second denomi rst fraction by x 3 x 1 nator so multiply the second fraction by x 1 1 x 3 x x 1 x 3 x 3 x 1 x 3 x 3 x 3 x 1 x 3 x 1 x 3 x x 1 x 3 x 1 x 3 x 3 x x 1 x 3 x2 x x2 3 x 3 x 1 x 3 x 3 x 1 x 3 x 3 x 1 x 3 6x 2 6x 2 2 x 2x 1 x 4x 3 x 1 x 1 x 1 x 3 6x x 3 2 x 1 2 x 3 x 1 x 3 x 1 x 1 6x x 3 2 x 1 x 1 2 x 3
6x2 18x 2x 2 6x2 16x 2 x 1 2 x 3 x 1 2 x 3
CHAPTER 6 Factoring
1 6 1 6 2x 5 1 6 2x 5 1 2x 5 1 2x 5 1 2x 5 2x 5 2x 5 12x 30 1 12x 31 2x 5 2x 5
3 x 2 3 x 2 x 4x 5 x 5 x 5 x 1 x 5 3 x 2 x 1 x 5 x 1 x 5 x 1
3 x 2 x 1 3 x2 3x 2 x 5 x 1 x 5 x 1 x2 3x 5 x 5 x 1
Practice
1: 2: 3: 4: 5: 1 1 2 x 5x 6 x 2x 3
5 2x 2x 5x 12 3x 12
1 2 2 x x 20 x x 12
1 5 2 24x 30 2x 2x 60
2 1 3 2 2 x 4x 2x 32 2x 10x 8 2x 3 x 4
6: 1 7:
1 1 x 3 x2 2x 3
CHAPTER 6 Factoring
Solutions
1: 1 1 1 1 x2 5x 6 x2 2x 3 x 2 x 3 x 1 x 3 1 x 1 1 x 2 x 3 x 1 x 1 x 3 x 2 1 x 1 1 x 2 x 2 x 2 x 3 x 1 2x 1 x 2 x 3 x 1 5 2x 5 2x 2x 3 x 4 3 x 4 2x 5x 12 3x 12 5 3 2x 2x 3 2x 3 x 4 3 3 x 4 2x 3
3:
5 3 2x 2x 3 15 4x2 6x 3 2x 3 x 4 3 2x 3 x 4 4x2 6x 15 3 2x 3 x 4
1 2 1 2 2 x x 20 x x 12 x 5 x 4 x 4 x 3 1 x 4 x 3 x 5 x 4 x 4 x 3 2 x 5 x 4 x 4 x 3 x 5 x 4 1 x 4 x 3 2 x 5 x 4 x 5 x 4 x 4 x 3
x2 x 12 2 x2 x 20 x 5 x 4 x 4 x 3 x2 x 12 2x2 2x 40 x 5 x 4 x 4 x 3 x2 x 28 x 5 x 4 x 4 x 3
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