if n < -91874156718365.66 or 1.888112624037396e+21 < n

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   43.4
2. Applied taylor to get
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)} \leadsto \frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)\]
   9.3
3. Taylor expanded around inf to get
   \[\color{red}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)} \leadsto \color{blue}{\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right)}\]
   9.3
4. Applied taylor to get
   \[\frac{1}{n \cdot x} - \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\right) \leadsto \left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}\]
   9.3
5. Taylor expanded around inf to get
   \[\color{red}{\left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}} \leadsto \color{blue}{\left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2}}\]
   9.3
6. Applied simplify to get
   \[\left(\frac{\log x}{{n}^2 \cdot x} + \frac{1}{n \cdot x}\right) - \frac{1}{2} \cdot \frac{1}{n \cdot {x}^2} \leadsto \left(\frac{\frac{1}{n}}{x} - \frac{\frac{1}{2}}{{x}^2 \cdot n}\right) + \frac{\log x}{x \cdot \left(n \cdot n\right)}\]
   8.7

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7. Applied final simplification

if -91874156718365.66 < n < 1.888112624037396e+21

1. Started with
   \[{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\]
   6.6
2. Using strategy rm
   6.6
3. Applied add-cube-cbrt to get
   \[\color{red}{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}} \leadsto \color{blue}{{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}^3}\]
   6.6
4. Using strategy rm
   6.6
5. Applied add-cube-cbrt to get
   \[{\color{red}{\left(\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right)}}^3 \leadsto {\color{blue}{\left({\left(\sqrt[3]{\sqrt[3]{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}}\right)}^3\right)}}^3\]
   6.6