x^3+8/x^3-2x^2+4x divided by x^4-16/x^2+4x+4

Question

I am just getting back into school and this is my first math class in like... 7 years! I think remember how to do this stuff, bu ti need some guidance.

Answer 1

(x^3+8/x^3-2x^2+4x) / (x^4-16/x^2+4x+4) =

(x^3+8/x^3-2x^2+4x)*(x^2+4x+4/x^4 - 16) =

(x^3 +2^3)/x(x^2 -2x +4)*(x+2)^2/[(x^2)^2 - 4^2)]=

(x+2)(x^2 -2x +3^2)/x(x^2 -2x +4)*(x+2)^2/(x-2)(x+2)(x^2+4) =

(x+2)^2*(x^2 -2x +3^2)/x(x^2 -2x +4)(x-2)(x^2+4)