## I apologize for the mistake in my previous response. Let's simplify the expression correctly.

To simplify (x^3 + 8)/(x^4 - 16), we can first factor the numerator and the denominator.

Numerator (x^3 + 8):

The numerator can be factored using the sum of cubes formula, which states that a^3 + b^3 = (a + b)(a^2 - ab + b^2). In this case, a = x and b = 2.

So, x^3 + 8 can be written as (x + 2)(x^2 - 2x + 4).

Denominator (x^4 - 16):

The denominator is actually the difference of squares. It can be written as (x^2)^2 - 4^2, which is (x^2 - 4)(x^2 + 4).

Now, the expression becomes [(x + 2)(x^2 - 2x + 4)] / [(x^2 - 4)(x^2 + 4)].

Next, we can cancel out the common factors in the numerator and denominator. Both the numerator and denominator have (x^2 - 4) as a factor.

Finally, after canceling out (x^2 - 4), we get the simplified expression:

(x + 2) / (x^2 + 4).

Therefore, the simplified expression is (x + 2) / (x^2 + 4).

I apologize again for the earlier mistake.