Initial program 13.6
\[wj - \frac{wj \cdot e^{wj} - x}{e^{wj} + wj \cdot e^{wj}}\]
- Using strategy
rm Applied div-sub13.6
\[\leadsto wj - \color{blue}{\left(\frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}} - \frac{x}{e^{wj} + wj \cdot e^{wj}}\right)}\]
Applied associate--r-7.2
\[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
Applied simplify6.7
\[\leadsto \color{blue}{\left(wj - \frac{wj}{wj + 1}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Taylor expanded around 0 1.0
\[\leadsto \color{blue}{\left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Applied simplify1.0
\[\leadsto \color{blue}{\frac{x}{(\left(e^{wj}\right) \cdot wj + \left(e^{wj}\right))_*} + (\left(1 - wj\right) \cdot \left(wj \cdot wj\right) + \left({wj}^{4}\right))_*}\]
Taylor expanded around inf 1.0
\[\leadsto \frac{x}{(\left(e^{wj}\right) \cdot wj + \left(e^{wj}\right))_*} + \color{blue}{\left(\left({\left(\frac{1}{wj}\right)}^{-4} + {wj}^{2}\right) - {wj}^{3}\right)}\]
Applied simplify1.0
\[\leadsto \color{blue}{\frac{x}{(\left(e^{wj}\right) \cdot wj + \left(e^{wj}\right))_*} + (\left(wj - wj \cdot wj\right) \cdot wj + \left({\left(\frac{1}{wj}\right)}^{-4}\right))_*}\]
