1 = A(x + 1)(x² + 1) + B(x² + 1) + (Cx + D)(x + 1)²

= Ax³ + Ax² + Ax + A + Bx² + B + Cx³ + 2Cx² + Cx + Dx² + 2D + D

= (A + C)x³ + (A + B + 2C + D)x² + (A + C + 2D)x + (A + B + D)

Equating constants

1 = A + B + D

Equating coefficients of x³

0 = A + C

Equating coefficients of x²

0 = A + B + 2C + D

Equating coefficients of x

0 = A + C + 2D

Solving we get

Thus,