TeX Quellcode:

\begin{array}{crclcl}\text{1. Zeile:} &-\dfrac{1}{x+10}+\dfrac{6}{5} &=& \dfrac{25}{x^2+20x+100} &\vert& \cdot (x+10) \cr \text{2. Zeile:} & -1+\dfrac{6}{5}\cdot (x+10) &=& \dfrac{25}{x^2+20x+100}\cdot (x+10) &\vert& \cdot 5 \cr \text{3. Zeile:} & -5+6(x+10) &=& \dfrac{125}{x^2+20x+100}\cdot (x+10) &\vert& \cdot \left(x^2+20x+100\right) \cr \text{4. Zeile:} & -5\left(x^2+20x+100\right)+6(x+10)\left(x^2+20x+100\right) &=& 125(x+10) \cr & -5x^2-100x-500+(6x+60)\left(x^2+20x+100\right) &=& 125x+1.250 \cr & -5x^2-100x-500+6x^3+120x^2+600x+60x^2+1.200x+6.000 &=& 125x+1.250 \cr & 6x^3+175x^2+1.700x+5.500 &=& 125x+1.250 &\vert& -125x-1.250 \cr & 6x^3+175x^2+1.575x+4.250 &=& 0 \cr & & \dots \cr & x_1 &=& -\dfrac{85}{6} \cr & x_2 &=& -10 \not\in\mathbb{D} \cr & x_3 &=& -5 \cr\cr& \mathbb{L} &=& \left\{-\dfrac{85}{6}; -5\right\}\end{array}