$$\left\{4 - \left\{x^2 + \left(3 - \frac{1}{x^2}\right)^{-1}\right\}^{-1}\right\}^{-1} = $$

A

$$\frac{3x^4}{12x^4 - 3x^2 + 1}$$

B

$$\frac{3x^4}{12x^2 + 1}$$

C

$$\frac{3x^2}{12x^2 + 3x + 1}$$

D

$$\frac{3x^2}{12x^4 + 3x^2 - 1}$$