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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 $(A,B)$.

 Jul 18, 2020
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If you let x go infinity, then you get 0 = A + B.

 

If you let x = 0, then you get -7/2 = A/(-2) + B.

 

The solution to this system is then A = 7/3, B = -7/3, so (A,B) = (7/3,-7/3).

 Jul 19, 2020

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