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

Aug 22, 2015

$y = \frac{x}{x - 3} = 1 + \frac{3}{x - 3}$

Hence the horizontal asymptote is $y = 1$

Explanation:

$y = \frac{x}{x - 3} = \frac{x - 3 + 3}{x - 3} = 1 + \frac{3}{x - 3}$

So as $x \to \pm \infty , \frac{3}{x - 3} \to 0$ and $1 + \frac{3}{x - 3} \to 1$

So the horizontal asymptote is $y = 1$