+0  
 
0
53
1
avatar

Find constants A and B such that
(x + 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).

 Feb 12, 2022
 #1
avatar+122390 
+1

We can use the method of partial fractions here

 

Note that  x^2  - x - 2   =   (x - 2)  (x + 1)

 

Multiply both sides by (x-2) (x + 1)   and we have this

 

x + 17  =  A(x + 1 ) + B ( x - 2)

 

1x + 17  = (A + B) x  + (A - 2B)          equate terms and we get this system of equations

 

A + B  =  1

A - 2B  = 17

 

Multiply the first equation by 2  and add to the second and we get that

 

3A  = 19

A = 19/3

 

And

 

A + B  = 1

19/3  + B  =1

B = 1  - 19/3  =      -16/3

 

 

cool cool cool

 Feb 12, 2022

9 Online Users