Question

Resolve : (+X+2 (x - 1)(x - 2) into partial fractions (OR)​

Answer 1

Answer:

Given faction is a proper fraction.

Let

(x−1)(x−2)(x−3)

x

2

=

x−1

A

+

x−2

B

+

x−3

C

....(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=

2

9

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

Hence, option 'B' is correct.