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{-3+3\sqrt{3}}{-1+\sqrt{3}} &=& 3\\\\3\cdot \left(\dfrac{-1+\sqrt{3}}{-1+\sqrt{3}}\right) &=& 3\\\\3 &=& 3 \end{array}