if alpha < 1.2543987852557203e+178

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   1.5
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   2.4
3. Using strategy rm
   2.4
4. Applied associate-/r* to get
   \[\color{red}{\frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{\frac{\frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\alpha + \left(2 + \beta\right)}}{\left(\alpha + 1.0\right) + \left(2 + \beta\right)}}{\alpha + \left(2 + \beta\right)}}\]
   1.5

if 1.2543987852557203e+178 < alpha

1. Started with
   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
   15.2
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}} \leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}}\]
   14.6
3. Applied taylor to get
   \[\frac{\frac{\left(\alpha + 1.0\right) + (\beta * \alpha + \beta)_*}{\alpha + \left(2 + \beta\right)}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{0}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   0
4. Taylor expanded around inf to get
   \[\frac{\color{red}{0}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)} \leadsto \frac{\color{blue}{0}}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}\]
   0
5. Applied simplify to get
   \[\color{red}{\frac{0}{\left(\left(\alpha + 1.0\right) + \left(2 + \beta\right)\right) \cdot \left(\alpha + \left(2 + \beta\right)\right)}} \leadsto \color{blue}{0}\]
   0