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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 18, 2021
 #1
avatar+33710 
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Cross multiply the right side to get

a(x+1)   + b (x-2) 

(x^2 -x-2)                              equate the L and R numerators

 

a (x+1) + b(x-2) = x+7

ax + a    + bx -2b   = x + 7    

    from this we can get    ax + bx = x        and   a -2b = 7

                                         a+ b =1                   a - 2b= 7         multiply red equation by -1 and add to second equation to get

                                               -3b = 6

                                                   b = -2       then   a = 3

 Apr 18, 2021
 #2
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That is correct! Nice jobsmiley

Guest Apr 18, 2021

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