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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 $(A,B)$

 Aug 29, 2021
 #1
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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, B = 7, so (A,B) = (7,7).

 Aug 29, 2021
 #2
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sorry, it says it's incorrect. @asinus can you help?

 Aug 29, 2021

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