23+55−3\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}5−323+5
= (23+55−3)(5+35+3)\left(\frac{2\sqrt{3} + \sqrt{5}}{\sqrt{5} - \sqrt{3}}\right)\left(\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}}\right)(5−323+5)(5+35+3)
= 215+6+5+155−3\frac{2\sqrt{15} + 6 + 5 + \sqrt{15}}{5 - 3}5−3215+6+5+15
= 315+112\frac{3\sqrt{15} + 11}{2}2315+11
