\(\frac{\frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}}{(e^{a \cdot \varepsilon} - 1)^*}\)
- Started with
\[\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}\]
58.5
- Applied simplify to get
\[\color{red}{\frac{\varepsilon \cdot \left(e^{\left(a + b\right) \cdot \varepsilon} - 1\right)}{\left(e^{a \cdot \varepsilon} - 1\right) \cdot \left(e^{b \cdot \varepsilon} - 1\right)}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}}\]
27.8
- Using strategy
rm 27.8
- Applied clear-num to get
\[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \color{red}{\frac{\varepsilon}{(e^{b \cdot \varepsilon} - 1)^*}} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \color{blue}{\frac{1}{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}}\]
27.8
- Using strategy
rm 27.8
- Applied add-cube-cbrt to get
\[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{1}{\color{red}{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{1}{\color{blue}{{\left(\sqrt[3]{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}\right)}^3}}\]
28.3
- Applied taylor to get
\[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^*}{(e^{a \cdot \varepsilon} - 1)^*} \cdot \frac{1}{{\left(\sqrt[3]{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}\right)}^3} \leadsto \frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot a} - 1)^* \cdot (e^{\varepsilon \cdot b} - 1)^*}\]
39.9
- Taylor expanded around 0 to get
\[\color{red}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot a} - 1)^* \cdot (e^{\varepsilon \cdot b} - 1)^*}} \leadsto \color{blue}{\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot a} - 1)^* \cdot (e^{\varepsilon \cdot b} - 1)^*}}\]
39.9
- Applied simplify to get
\[\frac{(e^{\varepsilon \cdot \left(b + a\right)} - 1)^* \cdot \varepsilon}{(e^{\varepsilon \cdot a} - 1)^* \cdot (e^{\varepsilon \cdot b} - 1)^*} \leadsto \frac{\frac{(e^{\varepsilon \cdot \left(a + b\right)} - 1)^*}{\frac{(e^{b \cdot \varepsilon} - 1)^*}{\varepsilon}}}{(e^{a \cdot \varepsilon} - 1)^*}\]
27.7
- Applied final simplification
