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

 Aug 2, 2019
 #1
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\(\text{textbook partial fractions problem}\\ x+7 = A(x+1) + B(x-2)\\ x+7 = (A+B)x + (A-2B)\\ A+B=1\\ B=1-A\\~\\ A-2B=7\\ A - 2(1-A) = 7\\ 3A - 2 = 7\\ A=3\\ B=-2\\~\\ \dfrac{x+7}{x^2-x-2}= \dfrac{3}{x-2}- \dfrac{2}{x+1}\)

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 Aug 2, 2019

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