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Find constants A and B such that

(x + 7)/(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).

 Dec 3, 2020
 #1
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This is a partial fractions  problem....note that   x^2   - 4x  +  3   = (x - 3) ( x -1)

 

So we have

 

(x + 7)                                 A                B

___________  =             _____     +  ______          multiply through by  ( x -3) (x -1)

(x -3) ( x -1)                     x  -1              x - 3

 

We have

 

x + 7 =  A(x -3)  +  B(x -1)   

 

x + 7 =  Ax  - 3A  + Bx   - B 

 

1x + 7 =  ( A + B)x  -3A -B 

 

Equating terms  gives us this system

 

A + B   =1

-3A - B  = 7         add these

 

-2A  = 8

A = -4

 

And

-4 + B  = 1

B  = 5

 

(A,B)  = (-4, 5)

 

 

cool cool cool

 Dec 3, 2020

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