into partial fraction.
Ans : x+1 + 1/x+1 - 4/x-1
Working :
Use long division to divide x^3 -x^2 +2x -6 by x^2 -1 (because it is improper fraction)
x^3 -x^2 +2x -6/x^2-1 = x+1 - 3x+5/x^2-1
3x+5 = A(x-1) + B(x+1)
3x+5 = (A+B)x - A+B
By comparing coefficients :
x^1 : A+B = 3
x^0 : -A+B = 5
A = -1
B = 4
Therefore,
x^3 -x^2 +2x -6/x^2-1 = x+1 + 1/x+1 - 4/x-1
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