Question 1031246: Write the partial decomposition of the rational expression:
(-x^2+2x+4)/(x(x+2)^2) = A/x + B/(x+2) + C/(x+2)^2
Thank you! Found 2 solutions by stanbon, Edwin McCravy:Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website! Write the partial decomposition of the rational expression:
(-x^2+2x+4)/(x(x+2)^2) = A/x + B/(x+2) + C/(x+2)^2
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Equate the numerators since the denominators are the same.
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-x^2 + 2x + 4 = A(x+2)^2 + Bx(x+2) + Cx
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-x^2 + 2x + 4 = Ax^2 + 4Ax + 4A + Bx^2 + 2Bx + Cx
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-x^2 + 2x + 4 = (A+B)x^2 + (4A + 2B + C)x + 4A
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Equate corresponding coefficients::
A+B = -1
4A + 2B + C = 2
4A = 4
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A = 1
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So, B = -2
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And C = 2-4+4 = 2
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Ans: 1/x - 2/(x+2) + 2/(x+2)^2
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Cheers,
Stan H. Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Multiply both sides by the LCD x(x+2)²
Substitute x=0
Substitute x=-2
Substitute x=1, A=1, C=2
So:
becomes:
Edwin