第73問 答え

$$\begin{align}&\frac{2\sqrt{3} + 3 \sqrt{2}}{2\sqrt{3} - 3\sqrt{2}}\\&=\frac{(2\sqrt{3} + 3 \sqrt{2})(2\sqrt{3} + 3\sqrt{2})}{(2\sqrt{3} - 3\sqrt{2})(2\sqrt{3} + 3\sqrt{2})}\\&=\frac{2^2 \times 3 + 2 \times 2 \times 3 \times \sqrt{6} + 3^2 \times 2}{(2\sqrt{3})^2 - (3\sqrt{2})^2}\\&=\frac{ 30 + 12\sqrt{6}}{12-18}\\&=\frac{ 30 + 12\sqrt{6}}{-6}\\&=-5 - 2 \sqrt{6}\end{align}$$