SOLUTION: Find the partical fraction decomposition for the following rational expression: 4x^2-5x-15/x(x+1)(x-5)

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Question 679682: Find the partical fraction decomposition for the following rational expression: 4x^2-5x-15/x(x+1)(x-5)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the partial fraction decomposition for the following rational expression: 4x^2-5x-15/x(x+1)(x-5)
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4x^2-5x-15/[x(x+1)(x-5)] = A/x + B/(x+1) + C/(x-5)
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4x^2-5x-15 = [A(x+1)(x-5)] + [Bx(x-5)] + [Cx(x+1)]
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4x^2-5x-15 = Ax^2-4Ax-5A + Bx^2 - 5Bx + Cx^2 + Cx
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4x^2-5x-15 = (A + B + C)x^2 + (-4A-5B+C)x + (-5A)
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Equation:
A + B + C = 4
-4A-5B+C = -5
-5A = -15
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A = 3
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Substitute 3 for A to get:
B + C = 1
-5B+C = 7
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Subtract and solve for "B":
6B = -6
B = -1
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Solve for "C":
C = 2
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4x^2-5x-15/[x(x+1)(x-5)] = 3/x - 1/(x+1) + 2/(x-5)
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Cheers,
Stan H.
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