TeX Quellcode:

\begin{array}{rclll}\dfrac{1}{x^2-81} &=& \dfrac{x}{x-9}-1 &\vert& -\dfrac{1}{x^2-81} \cr0 &=& -\dfrac{1}{x^2-81}+\dfrac{x}{x-9}-1 \cr0 &=& -\dfrac{1}{x^2-81}+\dfrac{x\cdot\left(x+9\right)}{\left(x-9\right)\left(x+9\right)}-1 \cr0 &=& \dfrac{-1+x^2+9x}{x^2-81}-1 &\vert& \cdot\left(x^2-81\right) \cr0 &=& -1+x^2+9x-1\cdot\left(x^2-81\right) \cr 0 &=& 9x+80 &\vert & -9x \cr -9x &=& 80 &\vert & :(-9) \cr x &=& -\dfrac{80}{9} \;\in\;\mathbb{D} \cr\cr \mathbb{L} &=& \left\{-\dfrac{80}{9}\right\} \end{array}