Simplify this expression: 11 + (x^3 - 8 / x^2 + 2x + 4) - x

as written, I get

x^3 - 8/x^2 + 2x + 4

If you mean

11 + (x^3 - 8) / (x^2 + 2x + 4) - x
then that's just
11 + x-2 - x
9

recall the factorization of the difference of cubes.