TeX Quellcode:

\begin{array}{crclll} & \dfrac{x^3+5x}{x^2+2}+3 &=& 0 &\vert & \cdot \left(x^2+2\right)\\\\& x^3+5x+3\left(x^2+2\right) &=& 0 \\& x^3+3x^2+5x+6 &=& 0 \\& x^3+2x^2 \;+\; x^2+5x+6 &=& 0 \\& x^2(x+2) \;+\; (x+2)(x+3) &=& 0 \\& (x+2)\left(x^2+x+3\right) &=& 0 &\vert & \text{Satz vom Nullprodukt}\\\text{Faktor 1:} & x+2 &=& 0 &\vert& -2\\& x &=& -2 \;\in\;\mathbb{D}\\\\\text{Faktor 2:} & x^2+x+3 &=& 0 &\vert & \text{p-q-Formel}\\& x^2 &=& -\dfrac{1}{2} \pm\sqrt{\left(\dfrac{1}{2}\right)^2-3}\\\end{array}