Initial program 0.0
\[\frac{-\left(f + n\right)}{f - n}\]
Initial simplification0.0
\[\leadsto -\frac{n + f}{f - n}\]
- Using strategy
rm Applied add-log-exp0.0
\[\leadsto -\color{blue}{\log \left(e^{\frac{n + f}{f - n}}\right)}\]
- Using strategy
rm Applied add-sqr-sqrt0.0
\[\leadsto -\log \color{blue}{\left(\sqrt{e^{\frac{n + f}{f - n}}} \cdot \sqrt{e^{\frac{n + f}{f - n}}}\right)}\]
Applied log-prod0.0
\[\leadsto -\color{blue}{\left(\log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right) + \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)\right)}\]
- Using strategy
rm Applied add-cbrt-cube0.0
\[\leadsto -\left(\color{blue}{\sqrt[3]{\left(\log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right) \cdot \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)\right) \cdot \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)}} + \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)\right)\]
- Using strategy
rm Applied pow1/20.0
\[\leadsto -\left(\sqrt[3]{\left(\log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right) \cdot \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)\right) \cdot \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)} + \log \color{blue}{\left({\left(e^{\frac{n + f}{f - n}}\right)}^{\frac{1}{2}}\right)}\right)\]
Applied log-pow0.0
\[\leadsto -\left(\sqrt[3]{\left(\log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right) \cdot \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)\right) \cdot \log \left(\sqrt{e^{\frac{n + f}{f - n}}}\right)} + \color{blue}{\frac{1}{2} \cdot \log \left(e^{\frac{n + f}{f - n}}\right)}\right)\]
Final simplification0.0
\[\leadsto \frac{-1}{2} \cdot \log \left(e^{\frac{f + n}{f - n}}\right) + \left(-\sqrt[3]{\log \left(\sqrt{e^{\frac{f + n}{f - n}}}\right) \cdot \left(\log \left(\sqrt{e^{\frac{f + n}{f - n}}}\right) \cdot \log \left(\sqrt{e^{\frac{f + n}{f - n}}}\right)\right)}\right)\]
