Simplify frac 2 sqrt 2 - sqrt 3 sqrt 2 sqrt 3 - JAMB Mathematics 2014 Question

(= \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)