Initial program 12.7
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
Initial simplification0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{\left(-2 \cdot v + 3\right) \cdot 0.125}{\frac{1 - v}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}\]
- Using strategy
rm Applied div-inv0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{\left(-2 \cdot v + 3\right) \cdot 0.125}{\color{blue}{\left(1 - v\right) \cdot \frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}}\]
Applied times-frac0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \color{blue}{\frac{-2 \cdot v + 3}{1 - v} \cdot \frac{0.125}{\frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}}\]
Simplified0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{-2 \cdot v + 3}{1 - v} \cdot \color{blue}{\left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)}\]
Taylor expanded around 0 0.4
\[\leadsto \color{blue}{\left(2 \cdot \frac{1}{{r}^{2}} - 1.5\right)} - \frac{-2 \cdot v + 3}{1 - v} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)\]
Simplified0.4
\[\leadsto \color{blue}{\left(\frac{2}{r \cdot r} - 1.5\right)} - \frac{-2 \cdot v + 3}{1 - v} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)\]
- Using strategy
rm Applied associate-/r*0.4
\[\leadsto \left(\color{blue}{\frac{\frac{2}{r}}{r}} - 1.5\right) - \frac{-2 \cdot v + 3}{1 - v} \cdot \left(\left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) \cdot 0.125\right)\]
Final simplification0.4
\[\leadsto \left(\frac{\frac{2}{r}}{r} - 1.5\right) - \left(\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot 0.125\right) \cdot \frac{v \cdot -2 + 3}{1 - v}\]
