TeX Quellcode:

\begin{array}{rclll} \dfrac{4x}{4x^3}-\left(\dfrac{1}{x^2}-4\right)+\dfrac{x^6-16}{2} &=& 0 \\\\\dfrac{1}{x^2}-\dfrac{1}{x^2}+4+\dfrac{x^6-16}{2} &=& 0 \\\\4+\dfrac{x^6-16}{2} &=& 0 &\vert & -4\\\\\dfrac{x^6-16}{2} &=& -4 &\vert & \cdot 2\\\\x^6-16 &=& -8 &\vert & +16\\x^6 &=& 8 &\vert & \pm\sqrt[6]{}\\x &=& \pm\sqrt[6]{8} \\x &=& \pm\left(2^3\right)^{\frac{1}{6}}\\x &=& \pm\left(2^3\right)^{\frac{1}{2}\cdot\frac{1}{3}}\\x &=& \pm2^{3\cdot\frac{1}{2}\cdot\frac{1}{3}}\\x &=& \pm2^{\frac{1}{2}}\\x &=& \pm\sqrt{2}\\\\x_1 &=& \sqrt{2}\;\in\;\mathbb{D}\\x_2 &=& -\sqrt{2}\;\in\;\mathbb{D}\end{array}