help with polynomial long division?

Question

use long division to determine the slant asymptote of f(x)=(x^3+x^2-10x+8)/(x^2+x-6)

Answer 1

..............x
............._________________
x^2+x-6 │x^3 + x^2 - 10x + 8
..............x^3 + x^2 - 6x
..............¯¯¯¯¯¯¯¯¯¯¯¯
..............................-4x + 8

f(x) = x + (-4x+8)/(x^2 + x - 6) = x - 4(x-2)/((x+3)(x-2))
= x - 4/(x+3)

as x → ∞ , 4/(x+3) → 0 and thus f(x) → x
So the asymptote is y=x

Answer 2

f(x) = x+(-4x+8)/(x^2+x-6)
As the second summand ==>0 the slant asymptote is y=x