$$\frac{2+\sqrt{-3}}{4+\sqrt{-3}}$$
$\text{Indeterminate}$
$$\frac{\left(2+\sqrt{-3}\right)\left(4-\sqrt{-3}\right)}{\left(4+\sqrt{-3}\right)\left(4-\sqrt{-3}\right)}$$
$$\frac{\left(2+\sqrt{-3}\right)\left(4-\sqrt{-3}\right)}{4^{2}-\left(\sqrt{-3}\right)^{2}}$$
$$\frac{\left(2+\sqrt{-3}\right)\left(4-\sqrt{-3}\right)}{16+3}$$
$$\frac{\left(2+\sqrt{-3}\right)\left(4-\sqrt{-3}\right)}{19}$$
$$\frac{8-2\sqrt{-3}+4\sqrt{-3}-\left(\sqrt{-3}\right)^{2}}{19}$$
$$\frac{8+2\sqrt{-3}-\left(\sqrt{-3}\right)^{2}}{19}$$
$$\frac{8+2\sqrt{-3}-\left(-3\right)}{19}$$
$$\frac{8+2\sqrt{-3}+3}{19}$$
$$\frac{11+2\sqrt{-3}}{19}$$
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