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Find constants A and B such that \(\frac{2x + 11}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\)for all x such that \(x\neq -1\) and \(x\neq 2\).

 Apr 2, 2024
 #1
avatar+128406 
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x^2 - x - 2 =  (x - 2) ( x + 1)

 

Multiply through by the factorization and we get

 

2x + 11 =  A(x + 1)  + B( x  -2)

 

2x + 11 = (A + B)x + (A - 2B)

 

Equating terms

 

A + B  = 2     →   B = 2 - A    (1)

A - 2B  = 11     (2)

 

Sub (1)  into (2)

 

A - 2 ( 2 -A)  = 11

A - 4 + 2A  = 11

3A = 15

A = 5

B = 2 - 5  =  -3

 

 

cool cool cool

 Apr 2, 2024

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