For this problem, we are given a certain fraction, and we need to rationalize and simplify it, so we can find the equivalent expression.
The original fraction is given below:
[tex]\frac{\sqrt{12}}{\sqrt{3}-3}[/tex]
We need to multiply both the denominator and numerator by sqrt(3) + 3. We have:
[tex]\begin{gathered} \frac{\sqrt{12}}{\sqrt{3}-3}\cdot\frac{\sqrt{3}+3}{\sqrt{3}+3}\\ \\ \frac{\sqrt{12}\sqrt{3}+3\sqrt{12}}{(\sqrt{3})^2-9}\\ \\ \frac{\sqrt{3\cdot4}\sqrt{3}+3\sqrt{3\cdot4}}{-6}\\ \\ \frac{2\cdot3+6\sqrt{3}}{-6}\\ \\ \frac{6+6\sqrt{3}}{-6}\\ \\ -1-\sqrt{3} \end{gathered}[/tex]
The correct answer is C
