$$\frac{ 3 \sqrt{ 2 } -2 \sqrt{ 3 } }{ 3 \sqrt{ 2 } +2 \sqrt{ 3 } }$$
$5-2\sqrt{6}\approx 0.101020514$
$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{\left(3\sqrt{2}+2\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}$$
$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)\left(3\sqrt{2}-2\sqrt{3}\right)}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{\left(3\sqrt{2}-2\sqrt{3}\right)^{2}}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{9\left(\sqrt{2}\right)^{2}-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{9\times 2-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{18-12\sqrt{2}\sqrt{3}+4\left(\sqrt{3}\right)^{2}}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{18-12\sqrt{6}+4\left(\sqrt{3}\right)^{2}}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{18-12\sqrt{6}+4\times 3}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{18-12\sqrt{6}+12}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{\left(3\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{3^{2}\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{9\left(\sqrt{2}\right)^{2}-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{9\times 2-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{18-\left(2\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{18-2^{2}\left(\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{18-4\left(\sqrt{3}\right)^{2}}$$
$$\frac{30-12\sqrt{6}}{18-4\times 3}$$
$$\frac{30-12\sqrt{6}}{18-12}$$
$$\frac{30-12\sqrt{6}}{6}$$
$$5-2\sqrt{6}$$
Show Solution
Hide Solution
$5-2\sqrt{6}$
