$$\frac{1}{\sqrt{4}-\sqrt{5}}$$
$-\sqrt{5}-2\approx -4.236067977$
$$\frac{1}{2-\sqrt{5}}$$
$$\frac{2+\sqrt{5}}{\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)}$$
$$\frac{2+\sqrt{5}}{2^{2}-\left(\sqrt{5}\right)^{2}}$$
$$\frac{2+\sqrt{5}}{4-5}$$
$$\frac{2+\sqrt{5}}{-1}$$
$$-2-\sqrt{5}$$
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