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-7.1
\[\leadsto \color{blue}{\left(wj - \frac{wj \cdot e^{wj}}{e^{wj} + wj \cdot e^{wj}}\right) + \frac{x}{e^{wj} + wj \cdot e^{wj}}}\]
Applied simplify6.5
\[\leadsto \color{blue}{\left(wj - \frac{wj}{wj + 1}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Taylor expanded around 0 1.1
\[\leadsto \color{blue}{\left(\left({wj}^{2} + {wj}^{4}\right) - {wj}^{3}\right)} + \frac{x}{e^{wj} + wj \cdot e^{wj}}\]
Applied simplify1.1
\[\leadsto \color{blue}{\frac{\frac{x}{e^{wj}}}{1 + wj} + \left({wj}^{4} + \left(wj \cdot wj\right) \cdot \left(1 - wj\right)\right)}\]
- Using strategy
rm Applied add-sqr-sqrt1.2
\[\leadsto \frac{\frac{x}{e^{wj}}}{1 + wj} + \left({wj}^{4} + \left(wj \cdot wj\right) \cdot \color{blue}{\left(\sqrt{1 - wj} \cdot \sqrt{1 - wj}\right)}\right)\]
Applied associate-*r*1.2
\[\leadsto \frac{\frac{x}{e^{wj}}}{1 + wj} + \left({wj}^{4} + \color{blue}{\left(\left(wj \cdot wj\right) \cdot \sqrt{1 - wj}\right) \cdot \sqrt{1 - wj}}\right)\]
