[tex]\displaystyle\\\text{We use the formula: }~~~\tan(2x)=\frac{2\tan(x)}{1-\tan^2(x)}\\ ---\\\\\frac{\tan(2x)}{\tan(x)}=\frac{\dfrac{2\tan(x)}{1-\tan^2(x)}}{\tan(x)}=\frac{2\tan(x)}{\tan(x)\Big(1-\tan^2(x)\Big)}=\boxed{\frac{2}{1-\tan^2(x)}}\\\\\\ \text{Correct answer:~~A.}[/tex]
