# How do you find the asymptotes for #(x^2 - 5x + 6)/(x - 3)#?

This function has no asymptotes. It has a hole at

It has no asymptotes.

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To find the asymptotes of the rational function ( \frac{x^2 - 5x + 6}{x - 3} ), first, check for any vertical asymptotes by identifying any values of ( x ) that make the denominator zero. In this case, ( x = 3 ) is the only value that makes the denominator zero, so there is a vertical asymptote at ( x = 3 ).

Next, to find the horizontal asymptote, compare the degrees of the numerator and denominator. 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 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, the degree of the numerator is 2 and the degree of the denominator is 1. Therefore, there is no horizontal asymptote.

So, the vertical asymptote is ( x = 3 ), and there is no horizontal asymptote.

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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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