Question 1043622
2 + ( 1 / (x-2) ) = (2x-3) / (x-2), then
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a(x+1) + b(x-1) = 2x-3
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ax+a +bx-b = 2x-3
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we have two equations in 2 unknowns
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1) ax +bx = 2x
2) a -b = -3
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solve 2) for b
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b = a +3
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substitute for b in equation 1)
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ax +(a+3)x = 2x
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2ax = -x
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a = -0.5
answer is A)
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check our answer
a = -0.5, then b = -0.5 +3 = 2.5
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substitute for a and b in the original equation
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(-0.5(x+1) + 2.5(x-1)) / (x-2) =
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(-0.5x -0.5 +2.5x -2.5) / (x-2) =
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(2x - 3) / (x-2) = 2 + ( 1 / (x-2) ) = (2x -3) / (x-2)
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our answer checks  :-)
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