Hello, gilagila!
We have: .
Then: .
. . . . . .
Let
Let
Therefore: .
x^2/(x-1)(x+1) = x^2/x^2-1 = 1,-1
Therefore,
x^2/(x-1)(x+1) = 1 + -1/(x-1)(x+1)
-1/(x-1)(x+1) = A/(x-1) + B/(x+1)
-1 = Ax + A + Bx - B
-1 = (A+B)x +A - B
A+B = 0, B = -A
-1 = A - B = A - (-A) = 2A
-1 = 2A, A = -1/2,
B = -(-1/2) = 1/2
Therefore,
x^2/(x-1)(x+1) = 1 - 1/2(x-1) + 1/2(x+1)
But somehow the answer given to me is
x^2/(x-1)(x+1) = 1 + 1/2(x-1) - 1/2(x+1)
Not sure which step I doing wrong, please help me on this. Thank you.