if x < -104399209346.08711 or 337865566.97886527 < x

1. Started with
   \[\frac{1}{x + 1} - \frac{1}{x}\]
   29.0
2. Applied taylor to get
   \[\frac{1}{x + 1} - \frac{1}{x} \leadsto \frac{1}{{x}^{3}} - \left(\frac{1}{{x}^2} + \frac{1}{{x}^{4}}\right)\]
   0.6
3. Taylor expanded around inf to get
   \[\color{red}{\frac{1}{{x}^{3}} - \left(\frac{1}{{x}^2} + \frac{1}{{x}^{4}}\right)} \leadsto \color{blue}{\frac{1}{{x}^{3}} - \left(\frac{1}{{x}^2} + \frac{1}{{x}^{4}}\right)}\]
   0.6
4. Applied simplify to get
   \[\frac{1}{{x}^{3}} - \left(\frac{1}{{x}^2} + \frac{1}{{x}^{4}}\right) \leadsto \frac{1}{{x}^3} - \left(\frac{1}{{x}^{4}} + \frac{\frac{1}{x}}{x}\right)\]
   0.1

---

5. Applied final simplification

if -104399209346.08711 < x < 337865566.97886527

1. Started with
   \[\frac{1}{x + 1} - \frac{1}{x}\]
   0.5
2. Using strategy rm
   0.5
3. Applied frac-sub to get
   \[\color{red}{\frac{1}{x + 1} - \frac{1}{x}} \leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]
   0.0
4. Applied simplify to get
   \[\frac{\color{red}{1 \cdot x - \left(x + 1\right) \cdot 1}}{\left(x + 1\right) \cdot x} \leadsto \frac{\color{blue}{x - \left(1 + x\right)}}{\left(x + 1\right) \cdot x}\]
   0.0
5. Applied simplify to get
   \[\frac{x - \left(1 + x\right)}{\color{red}{\left(x + 1\right) \cdot x}} \leadsto \frac{x - \left(1 + x\right)}{\color{blue}{x + {x}^2}}\]
   0.0