$$\frac{\sqrt{3}-\sqrt{7}}{\sqrt{13}+\sqrt{7}}$$
$\frac{\sqrt{39}+7-\sqrt{21}-\sqrt{91}}{6}\approx -0.146161618$
$$\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{13}-\sqrt{7}\right)}{\left(\sqrt{13}+\sqrt{7}\right)\left(\sqrt{13}-\sqrt{7}\right)}$$
$$\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{13}-\sqrt{7}\right)}{\left(\sqrt{13}\right)^{2}-\left(\sqrt{7}\right)^{2}}$$
$$\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{13}-\sqrt{7}\right)}{13-7}$$
$$\frac{\left(\sqrt{3}-\sqrt{7}\right)\left(\sqrt{13}-\sqrt{7}\right)}{6}$$
$$\frac{\sqrt{3}\sqrt{13}-\sqrt{3}\sqrt{7}-\sqrt{7}\sqrt{13}+\left(\sqrt{7}\right)^{2}}{6}$$
$$\frac{\sqrt{39}-\sqrt{3}\sqrt{7}-\sqrt{7}\sqrt{13}+\left(\sqrt{7}\right)^{2}}{6}$$
$$\frac{\sqrt{39}-\sqrt{21}-\sqrt{7}\sqrt{13}+\left(\sqrt{7}\right)^{2}}{6}$$
$$\frac{\sqrt{39}-\sqrt{21}-\sqrt{91}+\left(\sqrt{7}\right)^{2}}{6}$$
$$\frac{\sqrt{39}-\sqrt{21}-\sqrt{91}+7}{6}$$
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