# How do you find the horizontal asymptote for #(2x-4)/(x^2-4)#?

Asymptote is at

The first step for finding the asymptote is to factor EVERYTHING.

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To find the horizontal asymptote for (\frac{{2x - 4}}{{x^2 - 4}}):

- Determine the degrees of the numerator and denominator. The degree of the numerator is 1 and the degree of the denominator is 2.
- If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at (y = 0).
- If the degree of the numerator is equal to the degree of the denominator, divide the leading coefficients of both the numerator and the denominator to find the horizontal asymptote.
- If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
- In this case, since the degree of the numerator (1) is less than the degree of the denominator (2), the horizontal asymptote is at (y = 0).

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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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