Initial program 32.9
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
- Using strategy
rm Applied add-log-exp32.3
\[\leadsto \color{blue}{\log \left(e^{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}}\right)}\]
Taylor expanded around -inf 32.3
\[\leadsto \log \color{blue}{\left(2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{3}} + 1\right)\right)}\]
Simplified32.3
\[\leadsto \log \color{blue}{\left(\left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{5}}\right) + 1\right)}\]
- Using strategy
rm Applied add-exp-log32.3
\[\leadsto \color{blue}{e^{\log \left(\log \left(\left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{5}}\right) + 1\right)\right)}}\]
- Using strategy
rm Applied add-cube-cbrt32.3
\[\leadsto e^{\log \color{blue}{\left(\left(\sqrt[3]{\log \left(\left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{5}}\right) + 1\right)} \cdot \sqrt[3]{\log \left(\left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{5}}\right) + 1\right)}\right) \cdot \sqrt[3]{\log \left(\left(\frac{\frac{2}{x}}{x \cdot x} + \frac{2}{{x}^{5}}\right) + 1\right)}\right)}}\]
Final simplification32.3
\[\leadsto e^{\log \left(\left(\sqrt[3]{\log \left(\left(\frac{2}{{x}^{5}} + \frac{\frac{2}{x}}{x \cdot x}\right) + 1\right)} \cdot \sqrt[3]{\log \left(\left(\frac{2}{{x}^{5}} + \frac{\frac{2}{x}}{x \cdot x}\right) + 1\right)}\right) \cdot \sqrt[3]{\log \left(\left(\frac{2}{{x}^{5}} + \frac{\frac{2}{x}}{x \cdot x}\right) + 1\right)}\right)}\]
