If $$\frac{1}{x^{2}+a^{2}} = x^{2} - a^{2}$$, then the value of $$x$$ is:

A

$$\left(1 - a^{4}\right)^{\frac{1}{4}}$$

B

$$\left(a^{4} - 1\right)^{\frac{1}{4}}$$

C

a

D

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