TeX Quellcode:

\begin{array}{rcl} \dfrac{\sqrt{4\left(10+6\sqrt{3}\right)+3}+1}{2-\sqrt{10+6\sqrt{3}+2}} &=& 3\\\\\dfrac{\sqrt{40+24\sqrt{3}+3}+1}{2-\sqrt{12+6\sqrt{3}}} &=& 3\\\\\dfrac{\sqrt{43+24\sqrt{3}}+1}{2-\sqrt{9+6\sqrt{3}+3}} &=& 3\\\\\dfrac{\sqrt{16+24\sqrt{3}+27}+1}{2-\sqrt{\left(3+\sqrt{3}\right)^2}} &=& 3\\\\\dfrac{\sqrt{16+24\sqrt{3}+9\left(\sqrt{3}\right)^2}+1}{2-3-\sqrt{3}} &=& 3\\\\\dfrac{\sqrt{\left(4+3\sqrt{3}\right)^2}+1}{-1-\sqrt{3}} &=& 3\\\\\dfrac{4+3\sqrt{3}+1}{-1-\sqrt{3}} &=& 3\\\\\dfrac{5+3\sqrt{3}}{-1-\sqrt{3}} &=& 3\\\\\dfrac{5+3\sqrt{3}}{-1-\sqrt{3}} \cdot \dfrac{-1+\sqrt{3}}{-1+\sqrt{3}} &=& 3\\\\\dfrac{-5-3\sqrt{3}+5\sqrt{3}+3\cdot 3}{-1-3} &=& 3 \\\\\dfrac{4+2\sqrt{3}}{-2} &=& 3 \\\\-2-\sqrt{3} &=& 3\end{array}