Simpify \( \frac{\sqrt{3}-3 \sqrt{2}}{2 \sqrt{3}-2 \sqrt{2}} \)

Calculate or simplify the expression \( \frac{\sqrt{3}-3 \sqrt{2}}{2 \sqrt{3}-2 \sqrt{2}} \). Calculate the value by following steps: - step0: Calculate: \(\frac{\sqrt{3}-3\sqrt{2}}{2\sqrt{3}-2\sqrt{2}}\) - step1: Multiply by the Conjugate: \(\frac{\left(\sqrt{3}-3\sqrt{2}\right)\left(2\sqrt{3}+2\sqrt{2}\right)}{\left(2\sqrt{3}-2\sqrt{2}\right)\left(2\sqrt{3}+2\sqrt{2}\right)}\) - step2: Multiply the numbers: \(\frac{\left(\sqrt{3}-3\sqrt{2}\right)\left(2\sqrt{3}+2\sqrt{2}\right)}{4}\) - step3: Factor the expression: \(\frac{\left(\sqrt{3}-3\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)\times 2}{2\times 2}\) - step4: Reduce the fraction: \(\frac{\left(\sqrt{3}-3\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}{2}\) - step5: Multiply the numbers: \(\frac{-3-2\sqrt{6}}{2}\) - step6: Calculate: \(-\frac{3+2\sqrt{6}}{2}\) The simplified form of \( \frac{\sqrt{3}-3 \sqrt{2}}{2 \sqrt{3}-2 \sqrt{2}} \) is \( -\frac{3+2\sqrt{6}}{2} \).