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I have found this question in the Leithold´s book, but there´s no any worked example of how i can compute it in order to find the horizontal and vertical asympototes. enter image description here

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Another hint: you can find vertical asymptotes of a function like $p(x)/q(x)$ by looking for the values of $x$ which make $q(x) = 0$ (so long as they don't also make $p(x)=0$, of course).

As Nameless notes, the best hint for getting better answers would be to accept more answers.

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    Yes, they are the vertical ones.2012-12-29
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You can always find the horizontal ones by taking the limit of the function when $x\to\infty$: $\lim_{x\to\pm\infty}f(x)=\lim_{x\to\pm\infty}\frac{2}{\sqrt{x^2-4}}=0$ so $y=0$ is the only horizontal asymptote for $f(x)$. The vertical ones can be found by @Old John's comment.

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    Always good to know! +12013-02-28