For greater clarity, please enclose the divisor (x-2) inside parentheses. Thx.
Divide x-2 into 3x^2 + 7x + 1:
3x + 13
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x-2 / 3x^2 + 7x + 1
3x^2 - 6x
----------------
13x + 1
13x - 26
----------------
-27 (remainder)
-27
The quotient here is 3x + 13 - ------
x-2
The slant asymptote is the line y = 3x + 13. Note that -27 / (x-2) goes to zero as x grows large in either direction (positive or neg).
Note that you are looking for the "oblique" or "slant" asymptote here; there is no "horizontal" involved.
