Question

resolve into partial fractions (x ^ 2 - 2)/((x + 1) ^ 3)​

Answer 1

Answer:

Given faction is a proper fraction.

Let

(x−1)(x−2)(x−3)x 2 = x−1A + x−2B + x−3 ....(i)

Then

(x−1)(x−2)(x−3)x 2= (x−1)(x−2)(x−3)

A(x−2)(x−3)+B(x−3)(x−1)+C(x−1)(x−2)

⟹x

2

=A(x−2)(x−3)+B(x−3)(x−1)+C(x−1)(x−2) ....(ii)

Substituting x−1=0orx=1 in (ii), we get

1

2

=a(1−2)(1−3)+0+0

⟹A=

2

1

Substituting x−2=0 or x=2 in (ii), we get

2

2

=0+B(2−3)(2−1)+0

∴B=−4

Substituting x−3=0 or x=3 in (ii), we get

3

2

=0+0+C(3−1)(3−2)

∴C= 29

Substituting the value of A, B, and C in (i) then

(x−1)(x−2)(x−3)x 2

=

2(x−1)1− (x−2)4+ 2(x−3)9