The value of 1a^2 + ax + x^2 - 1a^2 - ax + x^2 + 2axa^4 + a^2x^2 + x^4 is?

Answer: Option D

$$\frac{1}{a^2+ax+x^2}$$   $$-$$ $$\frac{1}{a^2-ax+x^2}$$   $$+$$ $$\frac{2ax}{a^4+a^2{x}^2+x^4}$$
$$=\frac{a^2-ax+x^2-a^2-ax-x^2}{\left(a^2+x^2+ax\right)\left(a^2+x^2-ax\right)}+$$       $$\frac{2ax}{a^4+a^2{x}^2+x^4}$$
$$\begin{array}{rl}& =\frac{-2ax}{{\left(a^2+x^2\right)}^2-{\left(ax\right)}^2}+\frac{2ax}{a^4+x^4+a^2{x}^2}\\ & =\frac{-2ax}{a^4+x^4+2a^2{x}^2-a^2{x}^2}+\frac{2ax}{a^4+x^4+a^2{x}^2}\\ & =\frac{-2ax}{a^4+x^4+a^2{x}^2}+\frac{2ax}{a^4+x^4+a^2{x}^2}\\ & =0\end{array}$$