1. The problem is to simplify or understand the expression $\tan(x-\frac{\pi}{6})$. 2. We use the tangent subtraction formula: $$\tan(a-b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$$ where $a = x$ and $b = \frac{\pi}{6}$. 3. Recall that $\tan \frac{\pi}{6} = \frac{1}{\sqrt{3}}$. 4. Substitute into the formula: $$\tan\left(x - \frac{\pi}{6}\right) = \frac{\tan x - \frac{1}{\sqrt{3}}}{1 + \tan x \cdot \frac{1}{\sqrt{3}}}$$ 5. This expression shows how to write $\tan(x-\frac{\pi}{6})$ in terms of $\tan x$. 6. This formula is useful for evaluating or simplifying expressions involving tangent of angle differences. Final answer: $$\tan\left(x - \frac{\pi}{6}\right) = \frac{\tan x - \frac{1}{\sqrt{3}}}{1 + \frac{\tan x}{\sqrt{3}}}$$