TeX Quellcode:
\begin{array}{crclll} & \dfrac{x^5-x^2}{x}+\dfrac{x^3-4x^4}{4} &=& 0 \\& \dfrac{x\left(x^4-x\right)}{x}+\dfrac{4\left(\frac{1}{4}x^3-x^4\right)}{4} &=& 0 \\& x^4-x+\dfrac{1}{4}x^3-x^4 &=& 0 \\& \dfrac{1}{4}x^3-x &=& 0 \\& x\left(\dfrac{1}{4}x^2-1\right) &=& 0 &\vert & \text{Satz vom Nullprodukt}\\\text{Faktor 1:} & x &=& 0 \;\not\in\;\mathbb{D}\\\\\text{Faktor 2:} & \dfrac{1}{4}x^2-1 &=& 0 &\vert & +1\\& \dfrac{1}{4}x^2 &=& 1 &\vert & :\dfrac{1}{4}\\& x^2 &=& 4 &\vert & \pm\sqrt{}\\& x &=& \pm\sqrt{4}\\\\& x_1 &=& 2\;\in\;\mathbb{D}\\& x_2 &=& -2\;\in\;\mathbb{D}\end{array}