TeX Quellcode:

\begin{array}{lrclclll} &-\dfrac{1}{8} &=& \dfrac{2x^2-2x}{x^3+2x^2-3x} & \vert & \cdot \left(x^3+2x^2-3x\right) \cr &-\dfrac{1}{8}(x^3+2x^2-3x) &=& 2x^2-2x \cr &-\dfrac{1}{8}x^3-\dfrac{1}{4}x^2+\dfrac{3}{8}x &=& 2x^2-2x & \vert& +\dfrac{1}{8}x^3+\dfrac{1}{4}x^2-\dfrac{3}{8}x \cr &0 &=& \dfrac{1}{8}x^3+\dfrac{9}{4}x^2-\dfrac{19}{8}x \cr &0 &=& x\left(\dfrac{1}{8}x^2+\dfrac{9}{4}x-\dfrac{19}{8}\right) & \vert & \textrm{Satz vom Nullpunkt} \cr\cr\text{Faktor 1:} & x_1 &=& 0\not\in\; \mathbb{D} \cr\cr \text{Faktor 2:} & \dfrac{1}{8}x^2+\dfrac{9}{4}x-\dfrac{19}{8} &=& 0 &\vert& :\dfrac{1}{8} \cr & x^2+18x-19 &=& 0 &\vert& \text{p-q-Formel} \cr &x_{2,3} &=& -9 \pm \sqrt{9^2+19} \cr &&=& -9 \pm \sqrt{100} \cr\cr &x_2 &=& -9+10 = 1\not\in\; \mathbb{D} \cr &x_3 &=& -9-10 = -19\in\mathbb{D} & & \rightarrow \quad P_2\left(-19 \mid -\dfrac{1}{8}\right)\end{array}