\(\dfrac{3-\sqrt{27}}{2\sqrt{3}-2}\)
\(=\dfrac{3\left(1-\sqrt{3}\right)}{2\sqrt{3}-2}\)
\(=\dfrac{6\sqrt{3}+6-18-6\sqrt{3}}{\left(2\sqrt{3}\right)^2-2^2}\)
\(=\dfrac{6\left(\sqrt{3}+1-3-\sqrt{3}\right)}{\left(2\sqrt{3}\right)^2-2^2}\)
\(=\dfrac{6\left[\left(\sqrt{3}-\sqrt{3}\right)+\left(1-3\right)\right]}{2^2\sqrt{3}^2-2^2}\)
\(=\dfrac{-12}{4\sqrt{3}^2-4}\)
\(=-\dfrac{12}{8}=-\dfrac{3}{2}\)
\(\dfrac{3-\sqrt{27}}{2\sqrt{3}-2}\)
\(=\dfrac{3-3\sqrt{3}}{2\sqrt{3}-2}\)
\(=\dfrac{3\left(1-\sqrt{3}\right)}{2\left(\sqrt{3}-1\right)}\)
\(=\dfrac{-3\left(\sqrt{3}-1\right)}{2\left(\sqrt{3}-1\right)}\)
\(=-\dfrac{3}{2}\)
