+0  
 
0
300
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 $(A,B)$.

 Aug 27, 2017
 #1
avatar+96035 
+1

\(\[\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\]\)

 

\( $x\neq -1$\)

 

and

 

\($x\neq 2$\)

 

 

This is a partial fractions problem.....we want to solve this

 

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

 

x + 7  = (A + B)x + (A - 2B)     equating coefficients, we have the following system

 

A + B  = 1    →   B  = 1 - A     (1)

 

A - 2B  = 7      (2)

 

Sub (1) into (2)  and we have

 

A - 2(1 - A)  = 7

3A - 2  = 7

3A  = 9

A  = 3

 

And B  = 1 - 3  =  -2

 

So  (A, B)  =  (3 , -2)

 

 

 

cool cool cool

 Aug 28, 2017

34 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.