Question 669506: How can I express the following expression in partial fractions:
9x^2 - 22x + 9 / x^3 - 4x^2 + 3x
Help me ASAP.
Thanks in advance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! express the following expression in partial fractions:
9x^2 - 22x + 9 / x^3 - 4x^2 + 3x
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x^3 - 4x^2 + 3x = x(x^2-4x+3)
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Rewrite:
9x^2-22x+9 /x^3 -4x^2+3x = a/x + bx+c/(x^2-4x+3)
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9x^2-22x+9 = a(x^2-4x+3) + (bx+c)x
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9x^2-22x+9 = ax^2 -4ax + 3a + bx^2 + cx
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9x^2 - 22x + 9 = (a+b)x^2 +(-4a+c)x + 3a
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Equate the coefficients of Like terms to get:
Equations:
a+b = 9
-4a+c = -22
3a = 9
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Solve for a, b, c:
a = 3
b = 9-a = 6
c = -22+4a = -10
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Partial-Fraction Form
Fraction = 3/x + (6x-10)/(x^2-4x+3)
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Cheers,
Stan H.
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