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
66
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 such that  \( x\neq -1\)  and \( x\neq 2\). Give your answer as the ordered pair \((A, B)\).

 Aug 2, 2019
 #1
avatar+5798 
+1

\(\text{textbook partial fractions problem}\\ x+7 = A(x+1) + B(x-2)\\ x+7 = (A+B)x + (A-2B)\\ A+B=1\\ B=1-A\\~\\ A-2B=7\\ A - 2(1-A) = 7\\ 3A - 2 = 7\\ A=3\\ B=-2\\~\\ \dfrac{x+7}{x^2-x-2}= \dfrac{3}{x-2}- \dfrac{2}{x+1}\)

.
 Aug 2, 2019

12 Online Users

avatar
avatar