[2x^2-8x/x^2-16] / [8x^2/(x+4)^2]

= x+4/x
right?

*** (x+4)/x

I had (x+4)/(4x)

(use brackets, (x+4)/x is different from x+4/x , I have been making assumptions when you skipped the brackets )

Ah, you're right. I reduced the 2 and 8 to a 1:4 ratio but forgot to put the 4 as a coefficient in the denominator.

To simplify the given expression, you'll need to follow a series of steps. Here's how you can approach it:

Step 1: Factorizing the expressions in the numerator and denominator:
In the numerator, you can factor out a common factor of 2x:
2x(x - 4)
In the denominator, you can factor the difference of squares:
(x^2 - 16) = (x + 4)(x - 4)

So now the expression becomes:
[2x(x - 4)/(x + 4)(x - 4)] / [8x^2/(x + 4)^2]

Step 2: Simplify the expression by canceling out common factors:
Since there is a (x - 4) term in both the numerator and the denominator, you can eliminate them:
2x/8x^2

Step 3: Simplify further:
To simplify the expression, cancel out the common factor of 2x from the numerator and denominator:
(2x)/(2x * 4x)
This leaves you with:
1/4x

Therefore, the simplified expression is (1/4x), not (x + 4)/x.