Question

Resolve
(2x-5) / (x+3)(x+1)²
into partial fractions.
​

Answer 1

Answer:

(x+3)(x+1)  

2

 

(2x−5)

​

=  

x+3

A

​

+  

x+1

B

​

+  

(x+1)  

2

 

C

​

 

⇒2x−5=A(x+1)  

2

+B(x+1)(x+3)+C(x+3)

⇒2x−5=A(x  

2

+2x+1)+B(x  

2

+4x+3)+C(x+3)

On comparing coefficients  

0=A+B,2=2A+4B+C,−5=A+3B+3C

⇒A=−  

4

11

​

,B=  

4

11

​

,C=−  

2

7

​

 

Hence,  

(x+3)(x+1)  

2

 

(2x−5)

​

=−  

4(x+3)

11

​

+  

4(x+1)

11

​

−  

2(x+1)  

2

 

7

​

Please mark me as brainlist if it helps you