X^3-16/x^3 - 3x^2 -4x

a) To simplify the expression (x^3 - 16) / (x^3 - 3x^2 - 4x), we can factor the numerator and denominator.

Numerator: x^3 - 16
This is a difference of cubes, which can be factored as (x - 2)(x^2 + 2x + 4).

Denominator: x^3 - 3x^2 - 4x
We can factor out an x from each term: x(x^2 - 3x - 4).
Then, we can factor the quadratic expression: x(x - 4)(x + 1).

Now, we can rewrite the expression as:
[(x - 2)(x^2 + 2x + 4)] / [x(x - 4)(x + 1)]

b) To simplify the expression (x^3 + x^2 - 3) / (x^3 + 2x - 3), we can factor the numerator and denominator.

Numerator: x^3 + x^2 - 3
This expression cannot be factored further.

Denominator: x^3 + 2x - 3
This expression cannot be factored further.

Therefore, the expression (x^3 + x^2 - 3) / (x^3 + 2x - 3) cannot be simplified any further.