3x^2-6x-24

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3x^2+2x-8
this is just simplifying multiplying and dividing i got this far:
(3x 2)(x 12)
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(3x-2)(x+4)

To simplify the given expression, we can simplify the numerator and denominator separately and then divide them.

Let's start with simplifying the numerator:
3x^2 - 6x - 24

To factorize this expression, we first look for common factors. In this case, there is a common factor of 3. We can factor out 3:
3(x^2 - 2x - 8)

Now we need to factorize the quadratic expression within the parentheses. We are looking for two numbers that multiply to give -8 and add up to -2. We can factorize it as follows:
3(x - 4)(x + 2)

Moving on to simplify the denominator:
3x^2 + 2x - 8

Again, we look for common factors, and here we can see that there are no common factors. So, this quadratic expression cannot be factored further.

Now we can rewrite the original expression with the simplified numerator and denominator:
(3(x - 4)(x + 2))/(3x^2 + 2x - 8)

At this point, we can cancel out the common factors (3) in the numerator and denominator:
(x - 4)(x + 2)/(x^2 + 2x - 8)

Therefore, the final simplified expression is:
(x - 4)(x + 2)/(x^2 + 2x - 8)