# How do you simplify #(v^2 + v - 12)/ (v^2 + 6v + 8) div (2v - 6)/( v +2)#?

the trynomial

is obtained by the product:

so

and

So you can rewrite

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To simplify the expression, we can start by factoring the numerator and denominator separately.

The numerator, v^2 + v - 12, can be factored as (v + 4)(v - 3).

The denominator, v^2 + 6v + 8, can be factored as (v + 2)(v + 4).

Next, we can rewrite the expression as [(v + 4)(v - 3)] / [(v + 2)(v + 4)] divided by (2v - 6) / (v + 2).

Now, we can simplify further by canceling out common factors.

Canceling out (v + 4) in the numerator and denominator, and (v + 2) in the numerator and denominator, we get (v - 3) / (v + 2) divided by (2v - 6) / 1.

Simplifying the expression, we have (v - 3) / (v + 2) divided by (2v - 6).

To divide by a fraction, we can multiply by its reciprocal.

Therefore, the simplified expression is (v - 3) / (v + 2) multiplied by 1 / (2v - 6).

This can be further simplified as (v - 3) / [(v + 2)(2v - 6)].

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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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