√(x^3+1)-√x^3
=[√(x^3+1)-√x^3][√(x^3+1)+√x^3]/[√(x^3+1)+√x^3]
=[√(x^3+1)]^2-[√x^3]^2/[√(x^3+1)+√x^3]
=(x^3+1-x^3/[√(x^3+1)+√x^3]
=1/[√(x^3+1)+√x^3]
√(x^3+1)-√x^3
=[√(x^3+1)-√x^3][√(x^3+1)+√x^3]/[√(x^3+1)+√x^3]
=[√(x^3+1)]^2-[√x^3]^2/[√(x^3+1)+√x^3]
=(x^3+1-x^3/[√(x^3+1)+√x^3]
=1/[√(x^3+1)+√x^3]