TeX Quellcode:

\begin{array}{rclll} \dfrac{\sqrt{4k+3}+1}{2-\sqrt{k+2}} &=& 3 &\vert & \cdot \left(2-\sqrt{k+2}\right) \\\\\sqrt{4k+3}+1 &=& 6-3\sqrt{k+2} &\vert & -1+3\sqrt{k+2} \\\sqrt{4k+3}+3\sqrt{k+2} &=& 5 &\vert & ()^2\\4k+3+6\sqrt{\left(4k+3\right)\left(k+2\right)}+9\left(k+2\right) &=& 25 \\6\sqrt{4k^2+11k+6}+13k+21 &=& 25 &\vert & -13k-21\\6\sqrt{4k^2+11k+6} &=& 4-13k &\vert & ()^2\\36\left(4k^2+11k+6\right) &=& 16-104k+169k^2 \\144k^2+396k+216 &=& 16-104k+169k^2 &\vert & -16+104k-169k^2\\-25k^2+500k+200 &=& 0 &\vert & :(-25)\\k^2-20k-8 &=& 0 &\vert & \text{p-q-Formel}\\k_{1,2} &=& 10\pm\sqrt{(-10)^2+8}\\k_{1,2} &=& 10\pm\sqrt{108}\\\\ k_1 &=& 10+6\sqrt{3}\;\in\;\mathbb{D}\\k_2 &=& 10-6\sqrt{3}\;\in\;\mathbb{D}\end{array}