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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 $(A,B)$.

 Dec 27, 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 = -7/3, B = 7/3, so (A,B) = (-7/3,7/3).

 Dec 27, 2021
 #2
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Thank you for helping but that answer is incorrect, anyone can please help.

Guest Dec 28, 2021
 #3
avatar+32989 
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Two ways to do it are as follows:

I'll leave you to solve the equations.

 Dec 28, 2021

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