How do you simplify #(x-3)/(2x-8)*(6x^2-96)/(x^2-9)#?

Question

Eva Adamson · Accepted Answer

#(3(x+4))/(x+3)#

#(x-3)/(2x-8) * (6x^2-96)/(x^2-9)#

factor out anything is able to be factored #(x-3)/(2(x-4)) * (6(x^2-16))/((x-3)(x+3))=(x-3)/(2(x-4)) * (6(x-4)(x+4))/((x-3)(x+3))#

divide out the common factors #(cancel(x-3))/(2(cancel(x-4))) * (6(cancel(x-4))(x+4))/((cancel(x-3))(x+3))=(6(x+4))/(2(x+3))=(3(x+4))/(x+3)#

To simplify these kinds of problems, just try and factor out anything you see that is able to be factored. You need to get in the habit of just working out the problem even though you don't know what's going to happen next. Many times there are common factors that you can just divide out.

Kennedy Adams · Answer

undefined To simplify the expression (x-3)/(2x-8)*(6x^2-96)/(x^2-9), we can factor the numerator and denominator and cancel out any common factors.

First, let's factor the numerator and denominator separately:

Numerator: (x-3) can't be factored further.
Denominator: (2x-8) can be factored as 2(x-4).
Denominator: (x^2-9) can be factored as (x-3)(x+3).

Now, let's rewrite the expression with the factored forms:

(x-3)/(2x-8)*(6x^2-96)/(x^2-9) = (x-3)/(2(x-4))*(6x^2-96)/((x-3)(x+3))

Next, we can cancel out the common factors:

(x-3) cancels out in the numerator and denominator.
(x-4) cancels out in the denominator and the (6x^2-96) term.

After canceling out the common factors, we are left with:

1/2 * 6(x+4)/(x+3)

Simplifying further:

3(x+4)/(x+3)