To find a slant (or oblique) asymptote, long-divide the numerator by the denominator; ignore the remainder. The polynomial part is your asymptote.
VerticalHorizontalSlantExamplesPurplemath What is a horizontal asymptote? A horizontal asymptote for a rational function is a horizontal line, derived from the rational function, that shows you where the graph is, or thereabouts, when the graph goes off to the sides. MathHelp.com...