TeX Quellcode:

\begin{array}{crclcl}\text{1. Zeile:} & \dfrac{12}{x}+3 &=& -\dfrac{x}{x+6}+\dfrac{11}{2} &\vert& \cdot x \cr\text{2. Zeile:} &12+3x &=& -\dfrac{x}{x+6}\cdot x +\dfrac{11}{2}\cdot x &\vert& \cdot (x+6) \cr \text{3. Zeile:} &12(x+6)+ 3x(x+6) &=& -x\cdot x+\dfrac{11}{2}\cdot x(x+6) &\vert& \cdot 2 \cr \text{4. Zeile:} & 24(x+6)+6x(x+6) &=& -2x^2+11x(x+6) \cr & 24x+144+6x^2+36x &=& -2x^2+11x^2+66x \cr & 6x^2+60x+144 &=& 9x^2+66x &\vert&-9x^2-66x \cr & -3x^2-6x+144 &=& 0 &\vert& :(-3) \cr & x^2+2x-48 &=& 0 &\vert& \text{p-q-Formel} \cr & x_{1,2} &=& -1 \pm\sqrt{(-1)^2+48} \cr & &=& -1\pm\sqrt{49} \cr\cr & x_1 &=& -1+7 = 6 \in \mathbb{D} \cr & x_2 &=& -1-7 = -8 \in \mathbb{D}\cr\cr & \mathbb{L} &=& \left\{-8;6\right\}\end{array}