$$\frac{ (1+ \sqrt{ 2 } ) }{ (1- \sqrt{ 2 } )(1+ \sqrt{ 2 } ) }$$
$-\sqrt{2}-1\approx -2.414213562$
$$\frac{1}{-\sqrt{2}+1}$$
$$\frac{-\sqrt{2}-1}{\left(-\sqrt{2}+1\right)\left(-\sqrt{2}-1\right)}$$
$$\frac{-\sqrt{2}-1}{\left(-\sqrt{2}\right)^{2}-1^{2}}$$
$$\frac{-\sqrt{2}-1}{\left(-1\right)^{2}\left(\sqrt{2}\right)^{2}-1^{2}}$$
$$\frac{-\sqrt{2}-1}{1\left(\sqrt{2}\right)^{2}-1^{2}}$$
$$\frac{-\sqrt{2}-1}{1\times 2-1^{2}}$$
$$\frac{-\sqrt{2}-1}{2-1^{2}}$$
$$\frac{-\sqrt{2}-1}{2-1}$$
$$\frac{-\sqrt{2}-1}{1}$$
$$-\sqrt{2}-1$$
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