Find constants A and B such that (2x - 17)/(x^2 - x - 2) = A/(x - 2) + B/(x + 1) for all x such that x neq -1 and x \neq 2. Give your answer as the ordered pair (A,B).
+128408 Partial Fractions
Note that x^2 - x - 2 = (x + 1) (x - 2) multiply through by these two factors and we get
2x - 17 = A(x + 1) + B(x - 2) simplify
2x - 17 = (A + B) x + [ A - 2B]
Equate terms
A + B = 2 (1)
A - 2B = -17 → -A + 2B = 17 (2)
Add (1)and (2) and we get
3B = 19
B = 19 / 3
And
A + 19/3 = 2
A = 2 - 19/3
A = 6/ 3 = 19 / 3 = -13 / 3
(A , B) = (-13 / 3 , 19 / 3)
