$$\frac{3\sqrt{2}-\sqrt{2}}{\sqrt{3}+4}$$
$-\frac{2\sqrt{2}\left(\sqrt{3}-4\right)}{13}\approx 0.493440693$
$$\frac{2\sqrt{2}}{\sqrt{3}+4}$$
$$\frac{2\sqrt{2}\left(\sqrt{3}-4\right)}{\left(\sqrt{3}+4\right)\left(\sqrt{3}-4\right)}$$
$$\frac{2\sqrt{2}\left(\sqrt{3}-4\right)}{\left(\sqrt{3}\right)^{2}-4^{2}}$$
$$\frac{2\sqrt{2}\left(\sqrt{3}-4\right)}{3-16}$$
$$\frac{2\sqrt{2}\left(\sqrt{3}-4\right)}{-13}$$
$$\frac{2\sqrt{2}\sqrt{3}-8\sqrt{2}}{-13}$$
$$\frac{2\sqrt{6}-8\sqrt{2}}{-13}$$
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$-\frac{2 \sqrt{2} {(\sqrt{3} - 4)}}{13} = --0.4934406933398773$
