1−252+32=(1−252+32)(2−322−32)\frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}} = \left( \frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}} \right) \left( \frac{2 - 3\sqrt{2}}{2 - 3\sqrt{2}} \right)2+321−25=(2+321−25)(2−322−32)
= 2−32−45+6104−62+62−18\frac{2 - 3\sqrt{2} - 4\sqrt{5} + 6\sqrt{10}}{4 - 6\sqrt{2} + 6\sqrt{2} - 18}4−62+62−182−32−45+610
= 2−32−45+610−14\frac{2 - 3\sqrt{2} - 4\sqrt{5} + 6\sqrt{10}}{-14}−142−32−45+610
= 114(32+45−2−610)\frac{1}{14}(3\sqrt{2} + 4\sqrt{5} - 2 - 6\sqrt{10})141(32+45−2−610) (dividing through with the minus sign)
