$$\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}$$
$\frac{2\sqrt{10}+7}{3}\approx 4.44151844$
$$\frac{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}$$
$$\frac{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{2}\right)^{2}}$$
$$\frac{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}{5-2}$$
$$\frac{\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}{3}$$
$$\frac{\left(\sqrt{5}+\sqrt{2}\right)^{2}}{3}$$
$$\frac{\left(\sqrt{5}\right)^{2}+2\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{3}$$
$$\frac{5+2\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^{2}}{3}$$
$$\frac{5+2\sqrt{10}+\left(\sqrt{2}\right)^{2}}{3}$$
$$\frac{5+2\sqrt{10}+2}{3}$$
$$\frac{7+2\sqrt{10}}{3}$$
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