Find constants A and B such that (x + 7)/(x^2 - x - 2) = A/(x - 2) + B/(x + 1) for all x such that x≠ -1 and x≠ 2 Give your answer as the ordered pair (A,B).
For this case we have the following expression: (x + 7) / (x ^ 2 - x - 2) = A / (x - 2) + B / (x + 1) Rewriting we have: (x + 7) / ((x-2) (x + 1)) = A / (x - 2) + B / (x + 1) We multiply the equality by (x-2) (x + 1): x + 7 = A (x + 1) + B (x - 2) Rewriting we have the following system of equations: A + B = 1 A - 2B = 7 Solving the system we have: A = 3 B = -2 Answer: constants A and B are: A = 3 B = -2
