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Find constants A and B such that (2x - 17)/(x^2 - x - 2) = A/(x - 2) + B/(x + 1) for all x such that x neq -1 and x \neq 2.  Give your answer as the ordered pair (A,B).

 Jun 26, 2022
 #1
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Partial Fractions

 

Note that      x^2 - x - 2 =   (x + 1) (x - 2)    multiply through by these two factors and we  get

 

2x - 17 = A(x + 1)   + B(x - 2)       simplify

 

2x - 17 =  (A + B) x  + [ A - 2B]

 

Equate terms

 

A + B = 2                 (1)

A - 2B = -17    →   -A + 2B  = 17    (2)

 

Add (1)and (2)  and we get

 

3B = 19

B = 19 / 3

 

And

 

A + 19/3  = 2

A = 2 - 19/3

A = 6/ 3  = 19 / 3   = -13  / 3

 

(A , B) =  (-13 /  3  , 19 /  3)

 

 

cool cool cool

 Jun 26, 2022

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