# What are the asymptotes for #f(x)= x/(x(x-2))#?

So there's one vertical asymptote (simple pole) at

The horizontal asymptote is

For any rational expression with polynomial numerator and denominator, there are usually vertical asymptotes whenever the denominator is zero.

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The function (f(x) = \frac{x}{x(x-2)}) has two vertical asymptotes at (x = 0) and (x = 2). There are no horizontal or slant asymptotes for this function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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