$$\frac{ 1 }{ 2 \sqrt{ 5 } -5 \sqrt{ 2 } }$$
$-\frac{\sqrt{2}}{6}-\frac{\sqrt{5}}{15}\approx -0.384773459$
$$\frac{2\sqrt{5}+5\sqrt{2}}{\left(2\sqrt{5}-5\sqrt{2}\right)\left(2\sqrt{5}+5\sqrt{2}\right)}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{\left(2\sqrt{5}\right)^{2}-\left(-5\sqrt{2}\right)^{2}}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{2^{2}\left(\sqrt{5}\right)^{2}-\left(-5\sqrt{2}\right)^{2}}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{4\left(\sqrt{5}\right)^{2}-\left(-5\sqrt{2}\right)^{2}}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{4\times 5-\left(-5\sqrt{2}\right)^{2}}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{20-\left(-5\sqrt{2}\right)^{2}}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{20-\left(-5\right)^{2}\left(\sqrt{2}\right)^{2}}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{20-25\left(\sqrt{2}\right)^{2}}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{20-25\times 2}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{20-50}$$
$$\frac{2\sqrt{5}+5\sqrt{2}}{-30}$$
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$\frac{-2 \sqrt{5} - 5 \sqrt{2}}{30} = -0.38477345889550185$
