\(\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}\)
- Started with
\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
2.0
- Applied simplify to get
\[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
2.6
- Using strategy
rm 2.6
- Applied *-un-lft-identity to get
\[\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{red}{\alpha + \left(2 + \beta\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\color{blue}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
2.6
- Applied *-un-lft-identity to get
\[\frac{\frac{\color{red}{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\frac{\color{blue}{1 \cdot \left(\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)\right)}}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
2.6
- Applied times-frac to get
\[\frac{\color{red}{\frac{1 \cdot \left(\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)\right)}{1 \cdot \left(\alpha + \left(2 + \beta\right)\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{\frac{1}{1} \cdot \frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
2.6
- Applied times-frac to get
\[\color{red}{\frac{\frac{1}{1} \cdot \frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{\frac{1}{1}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}}\]
2.0
- Applied simplify to get
\[\color{red}{\frac{\frac{1}{1}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)} \leadsto \color{blue}{\frac{1}{\left(\beta + 1.0\right) + \left(\alpha + 2\right)}} \cdot \frac{\frac{\left(\alpha + 1.0\right) + \left(\beta + \beta \cdot \alpha\right)}{\alpha + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}\]
2.0
