- Started with
\[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
54.7
- Applied simplify to get
\[\color{red}{\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}} \leadsto \color{blue}{\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}}\]
44.8
- Using strategy
rm 44.8
- Applied *-un-lft-identity to get
\[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\color{red}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\color{blue}{1 \cdot \left(\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
44.8
- Applied *-un-lft-identity to get
\[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\color{red}{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}}^2}{1 \cdot \left(\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{\color{blue}{\left(1 \cdot \left(\left(\beta + \alpha\right) + 2 \cdot i\right)\right)}}^2}{1 \cdot \left(\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
44.8
- Applied square-prod to get
\[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{\color{red}{{\left(1 \cdot \left(\left(\beta + \alpha\right) + 2 \cdot i\right)\right)}^2}}{1 \cdot \left(\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{\color{blue}{{1}^2 \cdot {\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}}{1 \cdot \left(\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
44.8
- Applied times-frac to get
\[\frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{red}{\frac{{1}^2 \cdot {\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{1 \cdot \left(\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\color{blue}{\frac{{1}^2}{1} \cdot \frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
44.8
- Applied times-frac to get
\[\frac{\color{red}{\frac{i \cdot \left(\beta + \left(i + \alpha\right)\right)}{\frac{{1}^2}{1} \cdot \frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0} \leadsto \frac{\color{blue}{\frac{i}{\frac{{1}^2}{1}} \cdot \frac{\beta + \left(i + \alpha\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}\]
44.8
- Applied associate-/l* to get
\[\color{red}{\frac{\frac{i}{\frac{{1}^2}{1}} \cdot \frac{\beta + \left(i + \alpha\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}} \leadsto \color{blue}{\frac{\frac{i}{\frac{{1}^2}{1}}}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}{\frac{\beta + \left(i + \alpha\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}}}\]
44.8
- Applied taylor to get
\[\frac{\frac{i}{\frac{{1}^2}{1}}}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2 - 1.0}{\frac{\beta + \left(i + \alpha\right)}{\frac{{\left(\left(\beta + \alpha\right) + 2 \cdot i\right)}^2}{\alpha \cdot \beta + i \cdot \left(\beta + \left(i + \alpha\right)\right)}}}} \leadsto \frac{\frac{i}{\frac{{1}^2}{1}}}{16 \cdot i}\]
0.2
- Taylor expanded around 0 to get
\[\frac{\frac{i}{\frac{{1}^2}{1}}}{\color{red}{16 \cdot i}} \leadsto \frac{\frac{i}{\frac{{1}^2}{1}}}{\color{blue}{16 \cdot i}}\]
0.2
- Applied simplify to get
\[\color{red}{\frac{\frac{i}{\frac{{1}^2}{1}}}{16 \cdot i}} \leadsto \color{blue}{\frac{1}{16}}\]
0
