Ex 1: Determine the Vertical and Slant Asymptotes of a Rational Function

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This video provides an example of how to determine the equations of the vertical and slant asymptotes of a rational function.
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Why is the remainder of the equation for the slant asymptote excluded? I don't understand.

msha
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Is the slant asymptote the same thing as a horizontal asymptote ?

carolineserrano