# How do you simplify and find the excluded values of #(v^2+4) / (v^2-3v-18)#?

Asymptote at

Excluded values mean asymptotes and holes. So let's look for them:

First, let's expand all our components:

Now we have our factors:

Case 1

Case 2

Just to check our work, let's graph the equation and see graph{y=(x^2+4)/((x-6)(x+3))}

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To simplify the expression (v^2+4) / (v^2-3v-18), we can factor the numerator and denominator. The numerator cannot be factored further, but the denominator can be factored as (v-6)(v+3).

Therefore, the simplified expression is (v^2+4) / (v-6)(v+3).

To find the excluded values, we need to identify the values of v that would make the denominator equal to zero. In this case, v cannot be equal to 6 or -3, as these values would result in division by zero.

Hence, the excluded values are v = 6 and v = -3.

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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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