SOLUTION: Can someone show me how to write the partial fraction decomposition of (2x-3)/(x^2-2x+1) I don't know how to do this type of problem.
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Question 849453: Can someone show me how to write the partial fraction decomposition of (2x-3)/(x^2-2x+1) I don't know how to do this type of problem. Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! partial fraction decomposition of (2x-3)/(x^2-2x+1)
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DEN = (x-1)^2
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(2x-3)/(x^2-2x+1) = A/(x-1)^2 + B/(x-1)
(2x-3)/(x^2-2x+1) = A/(x-1)^2 + B(x-1)/(x-1)^2
2x-3 = A + Bx - B
2x = Bx
B = 2
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A - B = -3
A = -1
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Check:
(2x-3)/(x^2-2x+1) = -1/(x-1)^2 + 2/(x-1) ?
(2x-3)/(x^2-2x+1) = -1/(x-1)^2 + 2*(x-1)/(x-1)^2 ?
(2x-3) = -1 + 2*(x-1) ?
2x-3 = 2x - 3 it's correct
