TeX Quellcode:
\begin{array}{crclcll}& 0 &=& \left(x^2-4\right)\cdot\ln\left(x^2+x-6\right) & \vert & \text{Satz vom Nullprodukt}\\\\\text{Faktor 1:} & x^2-4 &=& 0 &\vert &+4 \\& x^2 &=& 4 &\vert &\pm\sqrt{} \\& x &=& \pm\sqrt{4} \\\\& x_1 &=& 2 \not\in\mathbb{D} \\& x_2 &=& -2 \not\in\mathbb{D} \\\\\text{Faktor 2:} & \ln\left(x^2+x-6\right) &=& 0 &\vert& e^{*} \\& x^2+x-6 &=& 1&\vert& -1 \\& x^2+x-7 &=& 0 &\vert& \text{p-q-Formel} \\& x_{1,2} &=& -\dfrac{1}{2}\pm\sqrt{\dfrac{1}{4}+7} \\\\&& =& -\dfrac{1}{2}\pm\sqrt{\dfrac{29}{4}} \\\\& x_1 &=& -\dfrac{1}{2}+\dfrac{\sqrt{29}}{2} \approx 2{,}19 \;\in\;\mathbb{D} \\\\& x_2 &=& -\dfrac{1}{2}-\dfrac{\sqrt{29}}{2} \approx -3{,}19 \;\in\;\mathbb{D}\end{array}