1. (x³+8)/(x³-2x²+4)=(x+8)(x²-2x+4)/(x*(x²-2x+4)=(x+8)/x.
2. (8x³+1)/(4x²-2x+1)=(2x+1)(4x²-2x+1)/(4x²-2x+1)=2x+1.
3. ((x+8)/x)-(2x+1)=(x+8-(2x+1)*x)/x=(-2x²+8)/x=-2*(x²-4)/x.
4. (8x³-1)/(4x²+2x+4)=2x-1.
5. (x³-8)/(x³+2x²+4)=(x-8)/x.
6. (2x-1)+(x-8)/x=((2x-1)*x+x-8)/x=(2x²-8)/x=2*(x²-4)/x.
7. (-2*(x²-4)/x):(2*(x²-4)/x)=-1.