# What are the vertical and horizontal asymptotes of #f(x)=5/((x+1)(x-3))#?

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The vertical asymptotes of the function f(x) = 5/((x+1)(x-3)) are x = -1 and x = 3. There are no horizontal asymptotes for this function.

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The vertical asymptotes of the function ( f(x) = \frac{5}{{(x+1)(x-3)}} ) occur where the denominator equals zero. Therefore, the vertical asymptotes are at ( x = -1 ) and ( x = 3 ).

To find the horizontal asymptote, compare the degrees of the numerator and denominator. Since the degree of the numerator (0) is less than the degree of the denominator (2), the horizontal asymptote is at ( y = 0 ), which is the x-axis.

So, the vertical asymptotes are at ( x = -1 ) and ( x = 3 ), and 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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