rac2+32−3rac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}rac2+32−3
= (2+32−3)(2+32+3)\left( \frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}} \right) \left( \frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}} \right)(2−32+3)(2+32+3)
= rac2+6+6+32−6+6−3rac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}rac2+6+6+32−6+6−3
= rac5+26−1rac{5 + 2\sqrt{6}}{-1}rac5+26−1
= −5−26-5 - 2\sqrt{6}−5−26
