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 $(A,B)$.
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).
Thank you for helping but that answer is incorrect, anyone can please help.
Two ways to do it are as follows:
I'll leave you to solve the equations.
