$$\frac{(2\sqrt{2}+3\sqrt{5})}{(\sqrt{2}-\sqrt{5})}$$
$\frac{-5\sqrt{10}-19}{3}\approx -11.6037961$
$$\frac{\left(2\sqrt{2}+3\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)}{\left(\sqrt{2}-\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)}$$
$$\frac{\left(2\sqrt{2}+3\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)}{\left(\sqrt{2}\right)^{2}-\left(\sqrt{5}\right)^{2}}$$
$$\frac{\left(2\sqrt{2}+3\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)}{2-5}$$
$$\frac{\left(2\sqrt{2}+3\sqrt{5}\right)\left(\sqrt{2}+\sqrt{5}\right)}{-3}$$
$$\frac{2\left(\sqrt{2}\right)^{2}+2\sqrt{2}\sqrt{5}+3\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}}{-3}$$
$$\frac{2\times 2+2\sqrt{2}\sqrt{5}+3\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}}{-3}$$
$$\frac{4+2\sqrt{2}\sqrt{5}+3\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}}{-3}$$
$$\frac{4+2\sqrt{10}+3\sqrt{5}\sqrt{2}+3\left(\sqrt{5}\right)^{2}}{-3}$$
$$\frac{4+2\sqrt{10}+3\sqrt{10}+3\left(\sqrt{5}\right)^{2}}{-3}$$
$$\frac{4+5\sqrt{10}+3\left(\sqrt{5}\right)^{2}}{-3}$$
$$\frac{4+5\sqrt{10}+3\times 5}{-3}$$
$$\frac{4+5\sqrt{10}+15}{-3}$$
$$\frac{19+5\sqrt{10}}{-3}$$
$$\frac{-19-5\sqrt{10}}{3}$$
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