1. The problem asks us to find the exact value of \(\tan\left(\dfrac{7\pi}{12}\right)\) using an angle addition or subtraction formula.\n\n2. We express \(\dfrac{7\pi}{12}\) as a sum of angles for which the tangent values are known. One choice is \(\dfrac{7\pi}{12} = \dfrac{3\pi}{4} - \dfrac{\pi}{6}\).\n\n3. Using the tangent subtraction formula: \n$$\tan(a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$$\nHere, let \(a = \dfrac{3\pi}{4}\) and \(b = \dfrac{\pi}{6}\).\n\n4. Calculate \(\tan a = \tan\left(\dfrac{3\pi}{4}\right) = -1\), and \(\tan b = \tan\left(\dfrac{\pi}{6}\right) = \frac{1}{\sqrt{3}}\).\n\n5. Substitute into the formula:\n$$\tan\left(\dfrac{7\pi}{12}\right) = \frac{-1 - \frac{1}{\sqrt{3}}}{1 + (-1) \cdot \frac{1}{\sqrt{3}}} = \frac{-1 - \frac{1}{\sqrt{3}}}{1 - \frac{1}{\sqrt{3}}}$$\n\n6. Multiply numerator and denominator by \(\sqrt{3}\) to simplify:\n$$ = \frac{-\sqrt{3} - 1}{\sqrt{3} - 1}$$\n\n7. This matches the expression:\n$$\frac{-1 - \sqrt{3}}{1 - \sqrt{3}}$$\n(rearranged terms but equivalent).\n\n8. Comparing to the choices, this corresponds to option B.