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x² - 9 4x² - 12x + 36
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2x² - 8x + 6 x³ + 27
Factor each numerator and denominator:
Left numerator: x² - 9 = x² - 3² = (x - 3)(x + 3)
Left denominator: 2x² - 8x + 6 = 2(x² - 4x + 3) = 2(x - 3)(x - 1)
Right numerator: 4x² - 12x + 36 = 4(x² - 3x + 9)
Right denominator: x³ + 27 = x³ + 3³ = (x + 3)(x² - 3x + 9)
(x - 3)(x + 3) 4(x² - 3x + 9)
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2(x - 3)(x - 1) (x + 3)(x² - 3x + 9)
Indicate multiplication of numerators and denominators:
4(x - 3)(x + 3)(x² - 3x + 9)
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2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
Cancel 2 and 4
2
4(x - 3)(x + 3)(x² - 3x + 9)
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2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
1
Cancel the (x - 3)'s
2 1
4(x - 3)(x + 3)(x² - 3x + 9)
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2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
1 1
Cancel the (x + 3)'s
2 1 1
4(x - 3)(x + 3)(x² - 3x + 9)
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2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
1 1 1
Cancel the (x² - 3x + 9)'s
2 1 1 1
4(x - 3)(x + 3)(x² - 3x + 9)
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2(x - 3)(x - 1)(x + 3)(x² - 3x + 9)
1 1 1 1
2
———————
x - 1
Edwin
AnlytcPhil@aol.com
