Initial program 8.2
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
Initial simplification8.1
\[\leadsto \sqrt{e^{x} + 1}\]
- Using strategy
rm Applied add-cube-cbrt8.1
\[\leadsto \sqrt{\color{blue}{\left(\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}\right) \cdot \sqrt[3]{e^{x} + 1}}}\]
- Using strategy
rm Applied add-cube-cbrt8.1
\[\leadsto \sqrt{\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}} \cdot \sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}}\right)} \cdot \sqrt[3]{e^{x} + 1}}\]
- Using strategy
rm Applied add-sqr-sqrt8.1
\[\leadsto \sqrt{\left(\left(\sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}} \cdot \sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}}\right) \cdot \color{blue}{\left(\sqrt{\sqrt[3]{e^{x} + 1}} \cdot \sqrt{\sqrt[3]{e^{x} + 1}}\right)}}\]
Final simplification8.1
\[\leadsto \sqrt{\left(\left(\sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}} \cdot \sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{x} + 1} \cdot \sqrt[3]{e^{x} + 1}}\right) \cdot \left(\sqrt{\sqrt[3]{e^{x} + 1}} \cdot \sqrt{\sqrt[3]{e^{x} + 1}}\right)}\]
