Question

resolve 4x^2+11/(x^2-1)(x+2) into partial fractions.​

Answer 1

Answer:

Since x

2

+2 can not be factored

So,

(x−1)(x

2

+2)

2x

2

+3x+4

=

x−1

A

+

x

2

+2

Bx+C

Now cross multiply, 2x

2

+3x+4=A(x

2

+2)+(Bx+C)(x−1)

⇒2x

2

+3x+4=A(x

2

+2)+Bx

2

−Bx+Cx−C

⇒2x

2

+3x+4=(A+B)x

2

+(C−B)x+(2A+C)

Comparing the coefficients, A+B=2.....(1),C−B=3......(2) and 2A−C=4.......(3)

Adding the three equations, we get

3A=9⇒A=3

From (1), A+B=2⇒3+B=2⇒B=−1

From (3), 2A−C=4⇒6−C=4⇒C=2

A=3,B=−1,C=2

Hence,

(x−1)(x

2

+2)

2x

2

+3x+4

=

x−1

3

+

x

2

+2

−x+2