For $$a \neq 0$$, $$\left(\frac{1}{1 + a^2 + a^{-2}} + \frac{1}{1 + a^{-2} + a^{-4}}\right)^{-1} - 1 =$$

A

$$\frac{1}{a^2 + 1}$$

B

$$\frac{1}{a^4 + 1}$$

C

$$\frac{1}{(a^2 + 1)(a^4 + 1)}$$

D

$$\frac{1}{a^2(a^2 + 1)}$$