Question

Resolve into partial fraction x^3/ x-a x-b x-c

Answer 1

Answer:

LHS=

(x−a)(x−b)(x−c)

x

3

;RHS=1

=1+

x−a

A

+

x−b

B

+

x−c

C

=(x−a)(x−b)(x−c)

+A(x−b)(x−c)

+B(x−a)(x−c)

+c(x−a)(x−b)

(x−a)(x−b)(x−c)

x

3

=(x−a)(x−b)

(x−c)+A(x−b)(x−c)

+B(x−a)(x−c)

+C(x−a)(x−b)−−(1)

keeping x=a in equation (1)

a

3

=A(a−b)(a−c)

A=

(a−b)(a−c)

a

3