Rationalization with conjugate 3+23+\sqrt{2}3+2
13−2\frac{1}{3-\sqrt{2}}3−21
→ 1⋅[3+2][3−2][3+2]\frac{1 \cdot [3+\sqrt{2}]}{[3-\sqrt{2}][3+\sqrt{2}]}[3−2][3+2]1⋅[3+2]
= 3+29−32+32−4\frac{3+\sqrt{2}}{9 -3\sqrt{2} + 3\sqrt{2} - \sqrt{4}}9−32+32−43+2
= 3+29−2\frac{3+\sqrt{2}}{9-2}9−23+2 → 3+27\frac{3+\sqrt{2}}{7}73+2
= 37\frac{3}{7}73 + 27\frac{\sqrt{2}}{7}72
