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Find constants A and B such that
(4x - 11)/(x^2 - 4x + 3) = A/(x - 1) + B/(x - 3)
for all x such that x is not equal to 1 and x is not equal to 3. Give your answer as the ordered pair (A,B).

 Jun 28, 2022
 #1
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Note that    x^2 - 4x + 3 =   (x -3) (x - 1)    multiply through by this factor

 

4x - 11 =  A(x - 3) + B( x - 1)

 

4x - 11  = (A + B) x -3A - B

 

Equating terms

 

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

 

-3A - B  =   -11  →    3A + B =  11    (2)

 

Sub (1) into (2)

 

3A + 4 - A = 11

 

2A =  11 - 4

 

2A  = 7

 

A =  7/2                  B =  4 - 7/2   =   1/2

 

(A , B)  =  (7/2 , 1/2)

 

 

cool cool cool

 Jun 28, 2022

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