Initial program 39.7
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Initial simplification0.0
\[\leadsto \sqrt{e^{x} + 1}\]
- Using strategy
rm Applied flip3-+0.0
\[\leadsto \sqrt{\color{blue}{\frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]
- Using strategy
rm Applied cube-mult0.0
\[\leadsto \sqrt{\frac{{\left(e^{x}\right)}^{3} + \color{blue}{1 \cdot \left(1 \cdot 1\right)}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}\]
Applied *-un-lft-identity0.0
\[\leadsto \sqrt{\frac{\color{blue}{1 \cdot {\left(e^{x}\right)}^{3}} + 1 \cdot \left(1 \cdot 1\right)}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}\]
Applied distribute-lft-out0.0
\[\leadsto \sqrt{\frac{\color{blue}{1 \cdot \left({\left(e^{x}\right)}^{3} + 1 \cdot 1\right)}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}\]
Applied associate-/l*0.0
\[\leadsto \sqrt{\color{blue}{\frac{1}{\frac{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}{{\left(e^{x}\right)}^{3} + 1 \cdot 1}}}}\]
Final simplification0.0
\[\leadsto \sqrt{\frac{1}{\frac{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}{1 + {\left(e^{x}\right)}^{3}}}}\]
