If $$\tan(\alpha + \beta) = a, \tan(\alpha - \beta) = b$$, then the value of $$\tan 2 \alpha$$ is:

A

$$\frac{a + b}{1 - ab}$$

B

$$\frac{a + b}{1 + ab}$$

C

$$\frac{a - b}{1 + ab}$$

D

$$\frac{a - b}{1 - ab}$$