We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
107
1
avatar

Find constants A and B such that \(\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}.\)

for all x such that \(x\neq -1\) and \(x\neq -2\). Give your answer as the ordered pair (A, B).

 Apr 14, 2019
 #1
avatar+104648 
+1

x^2 - x - 2  factors as  (x -2) ( x + 1)

Multiply through by this factorization and we have that

 

1x + 7  = A( x + 1) + B( x - 2)    simplify

 

1x + 7  =  Ax + A  + Bx - 2B     equate coefficients

 

1x + 7  =  (A + B) x  + (A - 2B)

 

This implies that

 

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

A - 2B = 7   (2)

 

Add (1) and (2)  and we have that

 

-3B =  6

B = -2

 

And

 

A + B  = 1

A - 2  = 1

A = 3

 

So  (A, B)  = ( 3, -2)

 

 

cool cool cool

 Apr 14, 2019

9 Online Users

avatar