Initial program 12.3
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
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 clear-num0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{\left(-2 \cdot v + 3\right) \cdot 0.125}{\color{blue}{\frac{1}{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}}}}\]
Taylor expanded around inf 0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{\color{blue}{0.375 - 0.25 \cdot v}}{\frac{1}{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}}}\]
- Using strategy
rm Applied div-sub0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \color{blue}{\left(\frac{0.375}{\frac{1}{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}}} - \frac{0.25 \cdot v}{\frac{1}{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}}}\right)}\]
Simplified0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \left(\color{blue}{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{\frac{1 - v}{0.375}}} - \frac{0.25 \cdot v}{\frac{1}{\frac{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}{1 - v}}}\right)\]
Final simplification0.4
\[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \left(\frac{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}{\frac{1 - v}{0.375}} - \frac{v \cdot 0.25}{\frac{1}{\frac{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}{1 - v}}}\right)\]
