\(\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot {\left(\frac{\sqrt{\beta + \left(\alpha \cdot \beta + \left(\alpha + 1.0\right)\right)}}{\left(2 + \alpha\right) + \beta}\right)}^2\)
- Started with
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
3.5
- Applied simplify to get
\[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
4.3
- Using strategy
rm 4.3
- Applied *-un-lft-identity to get
\[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{red}{\alpha + \left(2 + \beta\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{blue}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
4.3
- Applied *-un-lft-identity to get
\[\frac{\frac{\color{red}{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\color{blue}{1 \cdot \left(\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)\right)}}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
4.3
- Applied times-frac to get
\[\frac{\color{red}{\frac{1 \cdot \left(\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)\right)}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
4.3
- Applied times-frac to get
\[\color{red}{\frac{\frac{1}{1} \cdot \frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{\frac{1}{1}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}}\]
3.6
- Applied simplify to get
\[\color{red}{\frac{\frac{1}{1}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)} \leadsto \color{blue}{\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)}} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}\]
3.6
- Using strategy
rm 3.6
- Applied add-sqr-sqrt to get
\[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{red}{\alpha + \left(2 + \beta\right)}} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}\]
4.0
- Applied add-sqr-sqrt to get
\[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{red}{\alpha + \left(2 + \beta\right)}}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{blue}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
4.5
- Applied add-sqr-sqrt to get
\[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\color{red}{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\color{blue}{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
4.5
- Applied square-undiv to get
\[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\color{red}{\frac{{\left(\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}\right)}^2}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\color{blue}{{\left(\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}\]
4.5
- Applied square-undiv to get
\[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \color{red}{\frac{{\left(\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}{{\left(\sqrt{\alpha + \left(2 + \beta\right)}\right)}^2}} \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \color{blue}{{\left(\frac{\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}^2}\]
4.1
- Applied simplify to get
\[\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot {\color{red}{\left(\frac{\frac{\sqrt{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{\sqrt{\alpha + \left(2 + \beta\right)}}}{\sqrt{\alpha + \left(2 + \beta\right)}}\right)}}^2 \leadsto \frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot {\color{blue}{\left(\frac{\sqrt{\beta + \left(\alpha \cdot \beta + \left(\alpha + 1.0\right)\right)}}{\left(2 + \alpha\right) + \beta}\right)}}^2\]
3.6
