\(\left(\frac{\frac{2}{r}}{r} - \left(4.5 - 3\right)\right) - \left(3 - v \cdot 2\right) \cdot \frac{{\left(w \cdot r\right)}^2}{\frac{1 - v}{0.125}}\)
- Started with
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
11.6
- Applied simplify to get
\[\color{red}{\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5} \leadsto \color{blue}{\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(w \cdot r\right)}^2}\]
0.3
- Applied taylor to get
\[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(w \cdot r\right)}^2 \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({w}^2 \cdot {r}^2\right)\]
16.4
- Taylor expanded around inf to get
\[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{red}{\left({w}^2 \cdot {r}^2\right)} \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left({w}^2 \cdot {r}^2\right)}\]
16.4
- Applied simplify to get
\[\color{red}{\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({w}^2 \cdot {r}^2\right)} \leadsto \color{blue}{\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{1 - v}{3 - 2 \cdot v}}}\]
0.3
- Using strategy
rm 0.3
- Applied div-inv to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\color{red}{\frac{1 - v}{3 - 2 \cdot v}}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\color{blue}{\left(1 - v\right) \cdot \frac{1}{3 - 2 \cdot v}}}\]
0.3
- Applied associate-/r* to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \color{red}{\frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\left(1 - v\right) \cdot \frac{1}{3 - 2 \cdot v}}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \color{blue}{\frac{\frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{1 - v}}{\frac{1}{3 - 2 \cdot v}}}\]
0.4
- Applied taylor to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{\frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{1 - v}}{\frac{1}{3 - 2 \cdot v}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{\frac{\left({w}^2 \cdot {r}^2\right) \cdot 0.125}{1 - v}}{\frac{1}{3 - 2 \cdot v}}\]
16.4
- Taylor expanded around inf to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{\frac{\color{red}{\left({w}^2 \cdot {r}^2\right)} \cdot 0.125}{1 - v}}{\frac{1}{3 - 2 \cdot v}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{\frac{\color{blue}{\left({w}^2 \cdot {r}^2\right)} \cdot 0.125}{1 - v}}{\frac{1}{3 - 2 \cdot v}}\]
16.4
- Applied simplify to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{\frac{\left({w}^2 \cdot {r}^2\right) \cdot 0.125}{1 - v}}{\frac{1}{3 - 2 \cdot v}} \leadsto \left(\frac{2}{r \cdot r} - \left(4.5 - 3\right)\right) - \frac{\left(\left(w \cdot w\right) \cdot r\right) \cdot \left(r \cdot 0.125\right)}{\frac{1 - v}{3 - 2 \cdot v}}\]
7.9
- Applied final simplification
- Applied simplify to get
\[\color{red}{\left(\frac{2}{r \cdot r} - \left(4.5 - 3\right)\right) - \frac{\left(\left(w \cdot w\right) \cdot r\right) \cdot \left(r \cdot 0.125\right)}{\frac{1 - v}{3 - 2 \cdot v}}} \leadsto \color{blue}{\left(\frac{\frac{2}{r}}{r} - \left(4.5 - 3\right)\right) - \left(3 - v \cdot 2\right) \cdot \frac{{\left(w \cdot r\right)}^2}{\frac{1 - v}{0.125}}}\]
0.3
- Removed slow pow expressions