TeX Quellcode:

\begin{array}{rclcll} -\dfrac{24}{25} &=& \dfrac{2}{x(x-5)}-1 & \vert & +1 \cr \dfrac{1}{25} &=& \dfrac{2}{x(x-5)} \cr \dfrac{1}{25} &=& \dfrac{2}{x^2-5x} & \vert & \cdot \left(x^2-5x\right) \cr \dfrac{x^2-5x}{25} &=& 2 & \vert & \cdot 25 \cr x^2-5x &=& 50 & \vert & -50 \cr x^2-5x-50 &=& 0 &\vert& \text{p-q-Formel} \cr x_{1,2} &=& \dfrac{5}{2} \pm \sqrt{\left(-\dfrac{5}{2}\right)^2+50} \cr &=& \dfrac{5}{2} \pm \sqrt{\dfrac{225}{4}} \cr\cr x_1 &=& \dfrac{5}{2}+\dfrac{15}{2} = 10\in\mathbb{D} & & \rightarrow \quad P_2\left(10 \mid -\dfrac{24}{25}\right) \cr x_2 &=& \dfrac{5}{2}-\dfrac{15}{2} = -5\in\mathbb{D} & & \rightarrow \quad P_3\left(-5 \mid -\dfrac{24}{25}\right)\end{array}