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Find A and B such that (4x + 18)/(x^2 - 8x + 15) = A/(x - 3) + B/(x - 5) for all x besides 3 and 5. Express your answer as an ordered pair in the form (A,B).

 Jun 18, 2021
 #1
avatar+121048 
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Method of Partial Fractions  :

 

Note  that  (x^2  - 8x + 15)  = ( x -3) (x - 5)

Mutiply  the equation   by  this and we  get  that

 

4x + 18   = A(x - 5)  +  B (  x - 3)

 

4x + 18  =  (A + B)x  - ( 5A  + 3B)          equate  coefficients and  constants

 

A  +  B    =   4       ⇒    B  =  4  - A      (1)

-5A  - 3B  =  18          (2)

 

Sub (1)  into (2)

 

-5A  - 3(4 - A)  =  18

 

-5A  - 12  + 3A  = 18

 

-2A  -   12  =  18

 

-2A  =  30

 

A  = -15

 

B  = 4 - -15 =   19

 

(A,B)  = ( -15, 19)

 

 

cool cool cool

 Jun 18, 2021

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