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