if x < -1.7643470284436324e-06

1. Started with
   \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
   0.1
2. Using strategy rm
   0.1
3. Applied add-sqr-sqrt to get
   \[\sqrt{\frac{\color{red}{e^{2 \cdot x}} - 1}{e^{x} - 1}} \leadsto \sqrt{\frac{\color{blue}{{\left(\sqrt{e^{2 \cdot x}}\right)}^2} - 1}{e^{x} - 1}}\]
   0.1
4. Applied difference-of-sqr-1 to get
   \[\sqrt{\frac{\color{red}{{\left(\sqrt{e^{2 \cdot x}}\right)}^2 - 1}}{e^{x} - 1}} \leadsto \sqrt{\frac{\color{blue}{\left(\sqrt{e^{2 \cdot x}} + 1\right) \cdot \left(\sqrt{e^{2 \cdot x}} - 1\right)}}{e^{x} - 1}}\]
   0.0

if -1.7643470284436324e-06 < x

1. Started with
   \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
   60.1
2. Using strategy rm
   60.1
3. Applied flip-- to get
   \[\sqrt{\frac{e^{2 \cdot x} - 1}{\color{red}{e^{x} - 1}}} \leadsto \sqrt{\frac{e^{2 \cdot x} - 1}{\color{blue}{\frac{{\left(e^{x}\right)}^2 - {1}^2}{e^{x} + 1}}}}\]
   59.9
4. Applied associate-/r/ to get
   \[\sqrt{\color{red}{\frac{e^{2 \cdot x} - 1}{\frac{{\left(e^{x}\right)}^2 - {1}^2}{e^{x} + 1}}}} \leadsto \sqrt{\color{blue}{\frac{e^{2 \cdot x} - 1}{{\left(e^{x}\right)}^2 - {1}^2} \cdot \left(e^{x} + 1\right)}}\]
   59.9
5. Applied sqrt-prod to get
   \[\color{red}{\sqrt{\frac{e^{2 \cdot x} - 1}{{\left(e^{x}\right)}^2 - {1}^2} \cdot \left(e^{x} + 1\right)}} \leadsto \color{blue}{\sqrt{\frac{e^{2 \cdot x} - 1}{{\left(e^{x}\right)}^2 - {1}^2}} \cdot \sqrt{e^{x} + 1}}\]
   59.9
6. Applied simplify to get
   \[\color{red}{\sqrt{\frac{e^{2 \cdot x} - 1}{{\left(e^{x}\right)}^2 - {1}^2}}} \cdot \sqrt{e^{x} + 1} \leadsto \color{blue}{\sqrt{\frac{e^{x \cdot 2} - 1}{{\left(e^{x}\right)}^2 - 1}}} \cdot \sqrt{e^{x} + 1}\]
   59.9
7. Applied simplify to get
   \[\sqrt{\color{red}{\frac{e^{x \cdot 2} - 1}{{\left(e^{x}\right)}^2 - 1}}} \cdot \sqrt{e^{x} + 1} \leadsto \sqrt{\color{blue}{1}} \cdot \sqrt{e^{x} + 1}\]
   0.0