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There are numbers A and B for which A/(x - 1) + B/(x + 1) = (x + 3)/(x^2 - 1) for every number x other than 1 and -1. Find .A - B.

 
 Apr 30, 2021
 #1
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Note  x^2  - 1  = (x -1) (x + 1)

 

( x + 3)  / ( x^2 - 1)  =  A / ( x - 1)  +  B / ( x + 1)        multiply  through  by   ( x - 1) ( x + 1)

 

x + 3  =  A(x + 1)  + B  (x - 1)

 

x + 3 =  (A + B)x  + (A - B)

 

Equating terms .......this implies that  A - B =   3

 

 

cool cool cool

 
 Apr 30, 2021

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