For $$a, b > 0$$, let $$f(x) = \begin{cases} \frac{\tan((a+1)x) + b\tan x}{x}, & x < 0 \\ 3, & x = 0 \\ \frac{\sqrt{ax + b^2x^2} - \sqrt{ax}}{b\sqrt{ax}\sqrt{x}}, & x > 0 \end{cases}$$ be a continuous function at $$x = 0$$. Then $$\frac{b}{a}$$ is equal to :

A

6

B

4

C

5

D

8