[tex]\bf \cfrac{2x^2-5x+2}{x-3}\qquad
\begin{array}{r|rrrrll}
3&2&-5&2\\
&&6&3\\
--&--&--&--\\
&2&1&5
\end{array}
\\\\\\
quotient=\underline{2x+1}\qquad remainder=5
\\\\\\
\textit{thus oblique asymptote is }y=\underline{2x+1}[/tex]
oblique/slant asymptotes occur when the degree of the numerator is exactly 1 greater than that of the denominator
and the oblique asymptote occurs at the quotient of the rational expression, notice, since the denominator is just x - 3, doing a quick synthetic division will do to get the quotient.
