SOLUTION: Find the partial fraction expansion of the rational function F(x)=X/x^2-1

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Question 983639: Find the partial fraction expansion of the rational function F(x)=X/x^2-1
Answer by stanbon(75887) About Me  (Show Source):
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Find the partial fraction expansion of the rational function F(x)=X/x^2-1
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x/(x^2-1) = a/(x-1) + b/(x+1)
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[a(x+1) + b(x-1)]/(x^2-1)
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Equate the numerators::
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x = (a+b)x+(a-b)
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Equations:
a+b = 1
a-b = 0
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2a = 1
a = 1/2
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b = 1/2
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Ans:: x/(x^2-1) = (1/2)/(x+1)+(1/2)/(x-1)
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= 1/(2x+2) + 1/(2x-2)
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Cheers,
Stan H.
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