SOLUTION: What is the partial fraction decomposition of x/(x+3)(x-1)

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Question 693430: What is the partial fraction decomposition of x/(x+3)(x-1)
Answer by stanbon(75887) About Me  (Show Source):
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What is the partial fraction decomposition of x/(x+3)(x-1)
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x/[(x+3)(x-1)] = A/(x+3) + B/(x-1)
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= [A(x-1)+B(x+3)]/(x+3)(x-1)
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Equation the numerators:
x = (A+B)x + (3B-A)
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Equations:
A + B = 1
-A+3B = 0
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Add and solve for "B":
4B = 1
B = 1/4
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Solve for "A":
A + (1/4) = 1
A = 3/4
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Partial-fraction decomposition: (3/4)/(x+3) + (1/4)/(x-1)
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Cheers,
Stan H.