1. **State the problem:** Simplify the expression $$\frac{2 - \sqrt{3}}{-\sqrt{3} \cdot 2 + 1}$$. 2. **Rewrite the denominator:** The denominator is $$-\sqrt{3} \cdot 2 + 1 = -2\sqrt{3} + 1$$. 3. **Expression becomes:** $$\frac{2 - \sqrt{3}}{-2\sqrt{3} + 1}$$. 4. **Rationalize the denominator:** Multiply numerator and denominator by the conjugate of the denominator $$-2\sqrt{3} - 1$$ to eliminate the radical in the denominator. 5. **Multiply numerator:** $$ (2 - \sqrt{3})(-2\sqrt{3} - 1) = 2(-2\sqrt{3}) + 2(-1) - \sqrt{3}(-2\sqrt{3}) - \sqrt{3}(-1) $$ $$ = -4\sqrt{3} - 2 + 2 \cdot 3 + \sqrt{3} = -4\sqrt{3} - 2 + 6 + \sqrt{3} $$ $$ = (-4\sqrt{3} + \sqrt{3}) + (-2 + 6) = -3\sqrt{3} + 4 $$ 6. **Multiply denominator:** $$ (-2\sqrt{3} + 1)(-2\sqrt{3} - 1) = (-2\sqrt{3})^2 - (1)^2 = (4 \cdot 3) - 1 = 12 - 1 = 11 $$ 7. **Expression now:** $$ \frac{-3\sqrt{3} + 4}{11} $$ 8. **Final simplified form:** $$ \frac{4 - 3\sqrt{3}}{11} $$ This is the simplified form of the original expression.