TeX Quellcode:
\begin{array}{rclcl} \lg(x-1)+\lg(x+2) &=& 1 &\vert& \text{1. Logarithmengesetz} \cr \lg\left((x-1)(x+2)\right) &=& 1 &\vert& 10^{*} \cr 10^{\lg\left((x-1)(x+2)\right)} &=& 10^1 \cr (x-1)(x+2) &=& 10 \cr x^2+x-2 &=& 10 &\vert& -10 \cr x^2+x-12 &=& 0 &\vert& \text{p-q-Formel} \cr x_{1,2} &=& -\dfrac{1}{2} \pm \sqrt{\left(\dfrac{1}{2}\right)^2+12} \cr &=& -\dfrac{1}{2} \pm \sqrt{\dfrac{49}{4}} \cr\cr x_1 &=& -\dfrac{1}{2}+\dfrac{7}{2} = 3 \;\in\;\mathbb{D} \cr\cr x_2 &=& -\dfrac{1}{2}-\dfrac{7}{2} = -4 \;\not\in\; \mathbb{D} \\\\\mathbb{L} &=& \{3\}\end{array}