Question

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).

Answer 1

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