The value of ( x^1/3 + x^ - 1/3 ) ( x^2/3 - 1 + x^ - 2/3 ) is:

Answer: Option D

$$\begin{array}{rl}& \left(a+b\right)\left(a^2-ab+b^2\right)=a^3+b^3\\ & \therefore \left(x^{\frac{1}{3}}+x^{-\frac{1}{3}}\right)\left(x^{\frac{2}{3}}-1+x^{-\frac{2}{3}}\right)\\ & =\left(x^{\frac{1}{3}}+x^{-\frac{1}{3}}\right)\left({\left(x^{\frac{1}{3}}\right)}^2-x^{-\frac{1}{3}}.x^{\frac{1}{3}}+{\left(x^{-\frac{1}{3}}\right)}^2\right)\\ & ={\left(x^{\frac{1}{3}}\right)}^3+{\left(x^{-\frac{1}{3}}\right)}^3\\ & =x+x^{-1}\\ & =x+\frac{1}{x}\end{array}$$