TeX Quellcode:

\begin{array}{rclcll} \dfrac{7}{169} &=& \dfrac{x}{(x-2)^2} \cr\cr \dfrac{7}{169} &=& \dfrac{x}{x^2-4x+4} & \vert & \cdot \left(x^2-4x+4\right) \cr\cr \dfrac{7}{169}\cdot \left(x^2-4x+4\right) &=& x \cr\cr\dfrac{7}{169}x^2-\dfrac{28}{169}x+\dfrac{28}{169} &=& x & \vert & -x \cr\cr \dfrac{7}{169}x^2-\dfrac{197}{169}x+\dfrac{28}{169} &=& 0 & \vert & :\dfrac{7}{169} \cr\cr x^2-\dfrac{197}{7}x+4 &=& 0 &\vert& \text{p-q-Formel} \cr x_{1,2} &=& \dfrac{197}{14} \pm \sqrt{\left(-\dfrac{197}{14}\right)^2-4} \cr &=& \dfrac{197}{14} \pm \sqrt{\dfrac{38.025}{196}} \cr\cr x_1 &=& \dfrac{197}{14} + \dfrac{195}{14} = 28\in\mathbb{D} & & \rightarrow \quad P_2\left(28 \mid \dfrac{7}{169}\right) \cr x_2 &=& \dfrac{197}{14} - \dfrac{195}{14} = \dfrac{1}{7}\in\mathbb{D} & & \rightarrow \quad P_3\left(\dfrac{1}{7} \mid \dfrac{7}{169}\right)\end{array}