(1) Note x^2 - 1 = (x - 1) (x + 1)
x + 2 A B
____________ = _______ + _____ multiply through by (x - 1) ( x + 1)
(x - 1) ( x + 1) x - 1 x + 1
x + 2 = A ( x + 1) + B ( x - 1) simplify as
1x + 2 = (A + B)x + (A - B)
Equating terms we have that
A + B = 1
A - B = 2 add these equations
2A = 3
A = 3/2
And
3/2 + B = 1
B = -1/2
CORRECTED ANSWER !!!