Limits Continuity And Differentiability

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