$$\frac{ \sqrt{ 5 } - \sqrt{ 7 } }{ \sqrt{ 5 } + \sqrt{ 7 } }$$
$\sqrt{35}-6\approx -0.083920217$
$$\frac{\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}-\sqrt{7}\right)}{\left(\sqrt{5}+\sqrt{7}\right)\left(\sqrt{5}-\sqrt{7}\right)}$$
$$\frac{\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}-\sqrt{7}\right)}{\left(\sqrt{5}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$
$$\frac{\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}-\sqrt{7}\right)}{5-7}$$
$$\frac{\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}-\sqrt{7}\right)}{-2}$$
$$\frac{\left(\sqrt{5}-\sqrt{7}\right)^{2}}{-2}$$
$$\frac{\left(\sqrt{5}\right)^{2}-2\sqrt{5}\sqrt{7}+\left(\sqrt{7}\right)^{2}}{-2}$$
$$\frac{5-2\sqrt{5}\sqrt{7}+\left(\sqrt{7}\right)^{2}}{-2}$$
$$\frac{5-2\sqrt{35}+\left(\sqrt{7}\right)^{2}}{-2}$$
$$\frac{5-2\sqrt{35}+7}{-2}$$
$$\frac{12-2\sqrt{35}}{-2}$$
$$-6+\sqrt{35}$$
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