Given:

Using partial differentiation:

⇒1 = (Ax + B)(x² + 4)+(Cx + D)(x² + 1)

⇒ 1 = Ax³ +4Ax+ Bx² + 4B+ Cx³ + Cx + Dx² + D

⇒ 1 = (A+C)x³ +(B+D)x² +(4A+C)x + (4B+D)

Equating the coefficients of x, x², x³ and constant value. We get:

(a) A + C = 0 ⇒ C = -A

(b) B + D = 0 ⇒ B = -D

( c) 4A + C =0 ⇒ 4A = -C ⇒ 4A = A ⇒ 3A = 0 ⇒ A = 0 ⇒ C = 0

( d) 4B + D = 1 ⇒ 4B – B = 1 ⇒ B = 1/3 ⇒ D = -1/3

Put these values in equation (1)