Verified answer

(3x² - x + 4)/(x - 1)(x - 1)(x + 1)

=> (3x² - x + 4)/(x - 1)²(x + 1) = A/(x - 1) + B/(x - 1)² + C/(x + 1)

so, 3x² - x + 4 = A(x - 1)(x + 1) + B(x + 1) + C(x - 1)²

letting x = 1 we get:

6 = 2B

i.e. B = 3

letting x = -1 we get:

8 = 4C

i.e. C = 2

letting x = 0 we get:

4 = -A + B + C

=> 4 = -A + 3 + 2

i.e. A = 1

so, (3x² - x + 4)/(x - 1)²(x + 1) = 1/(x - 1) + 3/(x - 1)² + 2/(x + 1)

or, (3x² - x + 4)/(x - 1)(x² - 1) = 1/(x - 1) + 3/(x - 1)² + 2/(x + 1)

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