if beta < 5.53483801270981e+142

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   50.3
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{{\left(\beta + (i * 2 + \alpha)_*\right)}^2 - 1.0}}\]
   34.8

if 5.53483801270981e+142 < beta

1. Started with
   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
   63.0
2. Applied simplify to get
   \[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{{\left(\beta + (i * 2 + \alpha)_*\right)}^2 - 1.0}}\]
   53.6
3. Applied taylor to get
   \[\frac{\left(\frac{\left(\beta + \alpha\right) + i}{\beta + (i * 2 + \alpha)_*} \cdot (i * \left(\left(\beta + \alpha\right) + i\right) + \left(\alpha \cdot \beta\right))_*\right) \cdot \frac{i}{\beta + (i * 2 + \alpha)_*}}{{\left(\beta + (i * 2 + \alpha)_*\right)}^2 - 1.0} \leadsto \frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot i}{{\beta}^{3}} + \left(\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot \left(\alpha \cdot i\right)}{{\beta}^{4}} + \frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot {i}^2}{{\beta}^{4}}\right)\]
   41.8
4. Taylor expanded around inf to get
   \[\color{red}{\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot i}{{\beta}^{3}} + \left(\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot \left(\alpha \cdot i\right)}{{\beta}^{4}} + \frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot {i}^2}{{\beta}^{4}}\right)} \leadsto \color{blue}{\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot i}{{\beta}^{3}} + \left(\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot \left(\alpha \cdot i\right)}{{\beta}^{4}} + \frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot {i}^2}{{\beta}^{4}}\right)}\]
   41.8
5. Applied simplify to get
   \[\color{red}{\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot i}{{\beta}^{3}} + \left(\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot \left(\alpha \cdot i\right)}{{\beta}^{4}} + \frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\beta} + \left(\frac{1}{i} + \frac{1}{\alpha}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_* \cdot {i}^2}{{\beta}^{4}}\right)} \leadsto \color{blue}{(\left(\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\alpha} + \left(\frac{1}{\beta} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}{\beta}\right) * \left(\frac{i}{\beta \cdot \beta}\right) + \left(\frac{(\left(\frac{1}{i}\right) * \left(\frac{1}{\alpha} + \left(\frac{1}{\beta} + \frac{1}{i}\right)\right) + \left(\frac{1}{\beta \cdot \alpha}\right))_*}{\frac{{\beta}^{4}}{i}} \cdot \left(i + \alpha\right)\right))_*}\]
   7.0