Let

1 = A(x-1)(x²+1) + B(x+1)(x²+1) + (Cx + D)(x² - 1)

1 = A(x³ + x – x² -1) + B(x³ + x + x² + 1) + Cx³ + Dx² - Cx - D

1 = (A + B + C)x³ + (-A + B + D)x² + (A + B - C)x + (-A + B - D)

Equating the coefficients of x³, x², x and constant term, we get,

(A + B + C) = 0

(-A + B + C) = 0

(A + B - C) = 0

(-A + B - D) = 0

On solving these equations, we get,

A =

Therefore,