\(= \frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} - \sqrt{3}}\) \(= \frac{2\sqrt{2}(\sqrt{2}) + (2\sqrt{2})(-\sqrt{3})-\sqrt{3}(\sqrt{2})-\sqrt{3}(-\sqrt{3})}{(\sqrt{2})^2-(\sqrt{3})^2}\) \(= \frac{2 \times 2 - 2\sqrt{6} - \sqrt{6} + 3}{2 - 3}\) \(= \frac{4 - 3\sqrt{6} + 3}{-1}\) \(= \frac{7 - 3\sqrt{6}}{-1}\) \(= \frac{7}{-1} - \frac{3\sqrt{6}}{-1}\) \(= -7 + 3\sqrt{6}\) \(= 3\sqrt{6}-7\)