$$\frac{3-\sqrt{2}}{2\sqrt{3}+5}$$
$\frac{2\sqrt{6}+15-5\sqrt{2}-6\sqrt{3}}{13}\approx 0.187354371$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{\left(2\sqrt{3}+5\right)\left(2\sqrt{3}-5\right)}$$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{\left(2\sqrt{3}\right)^{2}-5^{2}}$$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{2^{2}\left(\sqrt{3}\right)^{2}-5^{2}}$$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{4\left(\sqrt{3}\right)^{2}-5^{2}}$$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{4\times 3-5^{2}}$$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{12-5^{2}}$$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{12-25}$$
$$\frac{\left(3-\sqrt{2}\right)\left(2\sqrt{3}-5\right)}{-13}$$
$$\frac{6\sqrt{3}-15-2\sqrt{3}\sqrt{2}+5\sqrt{2}}{-13}$$
$$\frac{6\sqrt{3}-15-2\sqrt{6}+5\sqrt{2}}{-13}$$
$$\frac{-6\sqrt{3}+15+2\sqrt{6}-5\sqrt{2}}{13}$$
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