if x < -0.0017322825953503614

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   0.8
2. Applied taylor to get
   \[\frac{e^{x}}{e^{x} - 1} \leadsto \frac{e^{x}}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\]
   30.7
3. Taylor expanded around 0 to get
   \[\frac{e^{x}}{\color{red}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}} \leadsto \frac{e^{x}}{\color{blue}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}}\]
   30.7
4. Using strategy rm
   30.7
5. Applied add-cbrt-cube to get
   \[\frac{e^{x}}{\color{red}{\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}} \leadsto \frac{e^{x}}{\color{blue}{\sqrt[3]{{\left(\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)\right)}^3}}}\]
   30.7
6. Applied add-cbrt-cube to get
   \[\frac{\color{red}{e^{x}}}{\sqrt[3]{{\left(\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)\right)}^3}} \leadsto \frac{\color{blue}{\sqrt[3]{{\left(e^{x}\right)}^3}}}{\sqrt[3]{{\left(\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)\right)}^3}}\]
   30.8
7. Applied cbrt-undiv to get
   \[\color{red}{\frac{\sqrt[3]{{\left(e^{x}\right)}^3}}{\sqrt[3]{{\left(\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)\right)}^3}}} \leadsto \color{blue}{\sqrt[3]{\frac{{\left(e^{x}\right)}^3}{{\left(\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)\right)}^3}}}\]
   30.8
8. Applied simplify to get
   \[\sqrt[3]{\color{red}{\frac{{\left(e^{x}\right)}^3}{{\left(\frac{1}{2} \cdot {x}^2 + \left(\frac{1}{6} \cdot {x}^{3} + x\right)\right)}^3}}} \leadsto \sqrt[3]{\color{blue}{{\left(\frac{e^{x}}{x + {x}^2 \cdot \left(x \cdot \frac{1}{6} + \frac{1}{2}\right)}\right)}^3}}\]
   0.1

if -0.0017322825953503614 < x

1. Started with
   \[\frac{e^{x}}{e^{x} - 1}\]
   60.4
2. Applied taylor to get
   \[\frac{e^{x}}{e^{x} - 1} \leadsto \frac{1}{2} + \left(\frac{1}{x} + \frac{1}{12} \cdot x\right)\]
   0.1
3. Taylor expanded around 0 to get
   \[\color{red}{\frac{1}{2} + \left(\frac{1}{x} + \frac{1}{12} \cdot x\right)} \leadsto \color{blue}{\frac{1}{2} + \left(\frac{1}{x} + \frac{1}{12} \cdot x\right)}\]
   0.1