TeX source:
\begin{array}{rclcll}\mathbb{D} &=& \mathbb{R}\setminus_{\{-\frac{1}{2}\}} \\ \\0 &=& \dfrac{e^y}{e^{2y+1}}-{e^y}^2 &\vert & +{e^y}^2 \\ \\{e^y}^2 &=& e^{y-(2y+1)} \\{e^y}^2 &=& e^{-y-1} &\vert& \ln() \\\ln\left({e^y}^2\right) &=& \ln\left(e^{-y-1}\right) \\y^2 &=& -y-1 &\vert& +y+1 \\y^2+y+1 &=& 0 &\vert &\text{p-q-Formel} \\y_{1,2} &=& -\dfrac{1}{2}\pm\sqrt{\left(\dfrac{1}{2}\right)^2-1} \\&=& -\dfrac{1}{2}\pm\sqrt{-\dfrac{3}{4}} \\\end{array}