\(\left(\frac{\frac{2}{r}}{r} - \left(4.5 - 3\right)\right) - \frac{\left(3 - v \cdot 2\right) \cdot 0.125}{\frac{1 - v}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}\)
- Started with
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
12.4
- 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
\[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot {\left(w \cdot r\right)}^2 \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({w}^2 \cdot {r}^2\right)\]
17.1
- Taylor expanded around inf to get
\[\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{red}{\left({w}^2 \cdot {r}^2\right)} \leadsto \left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \color{blue}{\left({w}^2 \cdot {r}^2\right)}\]
17.1
- Applied simplify to get
\[\color{red}{\left(\left(3 - 4.5\right) + \frac{2}{r \cdot r}\right) - \left(\frac{0.125}{1 - v} \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left({w}^2 \cdot {r}^2\right)} \leadsto \color{blue}{\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{1 - v}{3 - 2 \cdot v}}}\]
0.4
- Using strategy
rm 0.4
- Applied add-sqr-sqrt to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{1 - v}{\color{red}{3 - 2 \cdot v}}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{1 - v}{\color{blue}{{\left(\sqrt{3 - 2 \cdot v}\right)}^2}}}\]
16.0
- Applied add-sqr-sqrt to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{\color{red}{1 - v}}{{\left(\sqrt{3 - 2 \cdot v}\right)}^2}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\frac{\color{blue}{{\left(\sqrt{1 - v}\right)}^2}}{{\left(\sqrt{3 - 2 \cdot v}\right)}^2}}\]
16.1
- Applied square-undiv to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\color{red}{\frac{{\left(\sqrt{1 - v}\right)}^2}{{\left(\sqrt{3 - 2 \cdot v}\right)}^2}}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{{\left(r \cdot w\right)}^2 \cdot 0.125}{\color{blue}{{\left(\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}\right)}^2}}\]
16.2
- Applied add-sqr-sqrt to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{\color{red}{{\left(r \cdot w\right)}^2 \cdot 0.125}}{{\left(\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}\right)}^2} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \frac{\color{blue}{{\left(\sqrt{{\left(r \cdot w\right)}^2 \cdot 0.125}\right)}^2}}{{\left(\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}\right)}^2}\]
16.2
- Applied square-undiv to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \color{red}{\frac{{\left(\sqrt{{\left(r \cdot w\right)}^2 \cdot 0.125}\right)}^2}{{\left(\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}\right)}^2}} \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - \color{blue}{{\left(\frac{\sqrt{{\left(r \cdot w\right)}^2 \cdot 0.125}}{\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}}\right)}^2}\]
16.2
- Applied taylor to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - {\left(\frac{\sqrt{{\left(r \cdot w\right)}^2 \cdot 0.125}}{\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}}\right)}^2 \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - {\left(\frac{w \cdot \left(\sqrt{0.125} \cdot r\right)}{\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}}\right)}^2\]
16.1
- Taylor expanded around 0 to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - {\left(\frac{\color{red}{w \cdot \left(\sqrt{0.125} \cdot r\right)}}{\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}}\right)}^2 \leadsto \left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - {\left(\frac{\color{blue}{w \cdot \left(\sqrt{0.125} \cdot r\right)}}{\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}}\right)}^2\]
16.1
- Applied simplify to get
\[\left(3 + \left(\frac{\frac{2}{r}}{r} - 4.5\right)\right) - {\left(\frac{w \cdot \left(\sqrt{0.125} \cdot r\right)}{\frac{\sqrt{1 - v}}{\sqrt{3 - 2 \cdot v}}}\right)}^2 \leadsto \left(\frac{2}{r \cdot r} - \left(4.5 - 3\right)\right) - \frac{\left(\left(r \cdot w\right) \cdot \sqrt{0.125}\right) \cdot \left(\left(r \cdot w\right) \cdot \sqrt{0.125}\right)}{\frac{1 - v}{3 - v \cdot 2}}\]
0.5
- Applied final simplification
- Applied simplify to get
\[\color{red}{\left(\frac{2}{r \cdot r} - \left(4.5 - 3\right)\right) - \frac{\left(\left(r \cdot w\right) \cdot \sqrt{0.125}\right) \cdot \left(\left(r \cdot w\right) \cdot \sqrt{0.125}\right)}{\frac{1 - v}{3 - v \cdot 2}}} \leadsto \color{blue}{\left(\frac{\frac{2}{r}}{r} - \left(4.5 - 3\right)\right) - \frac{\left(3 - v \cdot 2\right) \cdot 0.125}{\frac{1 - v}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}}\]
0.3
