Question

resolve 2x+3/x^2-2x-3 into partial fraction​

Answer 1

Step-by-step explanation:

Let I=

x

2

+2x−3

2x

2

+5x−11

=

x

2

+2x−3

2(x

2

+2x−3)+x−5

=2+

x

2

+2x−3

x−5

=2+

(x+3)(x−1)

x−5

Now

(x+3)(x−1)

x−5

=

(x−1)

A

+

(x+3)

B

⇒x−5=A(x+3)+B(x−1)

On comparing coefficients we get

1=A+B,−5=3A−B

⇒A=−1,B=2

Therefore

I=2−

x−1

1

+

x+3

2