$$6+ \sqrt{ 3 } \div 6- \sqrt{ 3 } =A+B \sqrt{ 3 }$$
$A=\frac{-\sqrt{3}\left(6B+5\right)+36}{6}$
$$36+\sqrt{3}-6\sqrt{3}=6A+6B\sqrt{3}$$
$$36-5\sqrt{3}=6A+6B\sqrt{3}$$
$$6A+6B\sqrt{3}=36-5\sqrt{3}$$
$$6A=36-5\sqrt{3}-6B\sqrt{3}$$
$$6A=-6\sqrt{3}B+36-5\sqrt{3}$$
$$\frac{6A}{6}=\frac{-6\sqrt{3}B+36-5\sqrt{3}}{6}$$
$$A=\frac{-6\sqrt{3}B+36-5\sqrt{3}}{6}$$
$$A=-\sqrt{3}B-\frac{5\sqrt{3}}{6}+6$$
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$B=-\frac{\sqrt{3}A}{3}+2\sqrt{3}-\frac{5}{6}$
$$6B\sqrt{3}=36-5\sqrt{3}-6A$$
$$6\sqrt{3}B=-6A+36-5\sqrt{3}$$
$$\frac{6\sqrt{3}B}{6\sqrt{3}}=\frac{-6A+36-5\sqrt{3}}{6\sqrt{3}}$$
$$B=\frac{-6A+36-5\sqrt{3}}{6\sqrt{3}}$$
$$B=-\frac{\sqrt{3}A}{3}+2\sqrt{3}-\frac{5}{6}$$
