$$2+ \sqrt{ 3 } - \frac{ 1 }{ 2+ \sqrt{ 3 } }$$
$2\sqrt{3}\approx 3.464101615$
$$2+\sqrt{3}-\frac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}$$
$$2+\sqrt{3}-\frac{2-\sqrt{3}}{2^{2}-\left(\sqrt{3}\right)^{2}}$$
$$2+\sqrt{3}-\frac{2-\sqrt{3}}{4-3}$$
$$2+\sqrt{3}-\frac{2-\sqrt{3}}{1}$$
$$2+\sqrt{3}-\left(2-\sqrt{3}\right)$$
$$2+\sqrt{3}-2-\left(-\sqrt{3}\right)$$
$$2+\sqrt{3}-2+\sqrt{3}$$
$$\sqrt{3}+\sqrt{3}$$
$$2\sqrt{3}$$
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