Initial program 4.4
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Simplified0.1
\[\leadsto \color{blue}{\sqrt{e^{x} + 1}}\]
- Using strategy
rm Applied flip3-+0.1
\[\leadsto \sqrt{\color{blue}{\frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]
Taylor expanded around -inf 0.1
\[\leadsto \sqrt{\frac{\color{blue}{{\left(e^{x}\right)}^{3}} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}\]
Simplified0.1
\[\leadsto \sqrt{\frac{\color{blue}{e^{x} \cdot \left(e^{x} \cdot e^{x}\right)} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}\]
Final simplification0.1
\[\leadsto \sqrt{\frac{\left(e^{x} \cdot e^{x}\right) \cdot e^{x} + 1}{\left(1 - e^{x}\right) + e^{x} \cdot e^{x}}}\]
