Question

resolve into partial fraction 1/x(x+1)​

Answer 1

(x−1)(x+2)

2

9

=

x−1

A

+

x+2

B

+

(x+2)

2

C

=>9=A(x+2)

2

+B(x−1)(x+2)+C(x−1) -(1)

For x=1,=>9=A(3)

2

+B(0)+C(0)

=>9=9A

=>A=1 - (2)

For x=−2,=>9=A(0)+B(0)+C(−2−1)

=>9=−3C

=>C=−3 -(3)

Now , we have found out value of A and C , to find value of B , put x = any real number .

Let x =0 , then equation (1) reduces to 9=4A−2B−C

=>9=4−2B

=>2=−2B

=>B=−1 -(4)

Therefore from (2),(3),(4) we get

(x−1)(x+2)

2

9

=

x−1

1

−

x+2

1

−

(x+2)

2

3