How do you find the horizontal asymptote $y = x / (x-3)$ ?

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Answer 1 · 2015-08-22T14:37:27

$y = x/(x-3) = 1 + 3/(x-3)$

Hence the horizontal asymptote is $y = 1$

$y = x/(x-3) = (x-3+3)/(x-3) = 1+3/(x-3)$

So as $x->+-oo, 3/(x-3) -> 0$ and $1+3/(x-3) -> 1$

So the horizontal asymptote is $y=1$

How do you find the horizontal asymptote y = x / (x-3)y = x / (x-3)?