+0  
 
0
73
1
avatar

Enter (A,B,C) in order below if A, B, and C are the coefficients of the partial fractions expansion of (2x^2 + 3x - 5)/(x(x^2 - 1)) = A/x + B/(x - 1) + C/(x + 1).

 Jul 20, 2022
 #1
avatar+124676 
+1

Note that  x (x^2 -1)  = (x)(x + 1) ( x - 1)

 

Multiply throght by ths  factorization and we have

 

2x^2  + 3x   - 5 =  A ( x - 1)(x + 1)  + B(x)(x + 1)  + C(x)(x - 1)         simplify

 

2x^2 + 3x  -5 =  A ( x^2 -1)  + B( x^2 + x)  + C(x^2 - x)

 

2x^2 +  3x - 5 =  (A + B + C)x^2  + (B - C)x  - A

 

Equating terms we have this syatem

 

A + B + C  =  2

B - C  = 3           (1)

A = 5

 

So

5 + B + C = 2 

B + C  =  -3     (2)

 

Adding (1) and (2)  we get  that  2B  = 0   so B =  0

 

So

 

5 + 0 + C  =2

C = 2 -5   =  -3

 

(A,B,C)  =  (5, 0 , -3)

 

 

cool cool cool

 Jul 20, 2022

8 Online Users