# How do you find the asymptotes for #y= (3(x+5))/((x+1)(x+2))#?

Horizontal asymptotes:

Vertical asymptote:

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To find the asymptotes of ( y = \frac{3(x+5)}{(x+1)(x+2)} ), you need to check for vertical and horizontal asymptotes.

Vertical asymptotes occur where the denominator equals zero, but the numerator does not. So, set the denominator equal to zero and solve for ( x ). These values of ( x ) will give you the vertical asymptotes.

Horizontal asymptotes can be found by analyzing the behavior of the function as ( x ) approaches positive or negative infinity. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater, there is no horizontal asymptote.

Compute these values to find the asymptotes of the given 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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