Simplify the rational expression below.

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

I am sure you meant:

(x^3+2x^2+4)/(x^3+8)
then
= (x+2)(x+2)/( (x+2)(x^2 - 2x + 4)
= (x+2)/)x^2 - 2x+4) , x ≠ -2