First of all you should factor your function since X^2 - 1 + 2 = (x+1)(x-1) + 2 which implies y = (x-1) + 2/(x+1) as long as x != -1.
dy/dx = 1 - 2/(x+1)^2 = 1 which implies
1 = 1 - 2/(x+1)^2 which implies
-2/(x+1)^2 = 0 which only happens when x tends to infinity (positive or negative) which implies that there is no solution (which confirms your answer).
Notice what happens when x -> infinity: the 2/(x+1) cancels out and you get y = x - 1 which is indeed parallel to y = x.