if x < -2.3631973f0 or 9.955491f0 < x

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   8.4
2. Applied taylor to get
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \leadsto 2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)\]
   0.8
3. Taylor expanded around inf to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
   0.8
4. Applied simplify to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3}}\]
   0.8

if -2.3631973f0 < x < 9.955491f0

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   0.1
2. Using strategy rm
   0.1
3. Applied flip-+ to get
   \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}} \leadsto \color{blue}{\frac{{\left(\frac{1}{x + 1} - \frac{2}{x}\right)}^2 - {\left(\frac{1}{x - 1}\right)}^2}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}}\]
   13.8
4. Using strategy rm
   13.8
5. Applied *-un-lft-identity to get
   \[\frac{{\left(\frac{1}{x + 1} - \frac{2}{x}\right)}^2 - {\left(\frac{1}{x - 1}\right)}^2}{\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}} \leadsto \frac{{\left(\frac{1}{x + 1} - \frac{2}{x}\right)}^2 - {\left(\frac{1}{x - 1}\right)}^2}{\color{blue}{1 \cdot \left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}\right)}}\]
   13.8
6. Applied difference-of-squares to get
   \[\frac{\color{red}{{\left(\frac{1}{x + 1} - \frac{2}{x}\right)}^2 - {\left(\frac{1}{x - 1}\right)}^2}}{1 \cdot \left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}\right)} \leadsto \frac{\color{blue}{\left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\right) \cdot \left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}\right)}}{1 \cdot \left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}\right)}\]
   13.8
7. Applied times-frac to get
   \[\color{red}{\frac{\left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\right) \cdot \left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}\right)}{1 \cdot \left(\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}\right)}} \leadsto \color{blue}{\frac{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}}{1} \cdot \frac{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}}\]
   0.1
8. Applied simplify to get
   \[\color{red}{\frac{\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}}{1}} \cdot \frac{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}} \leadsto \color{blue}{\left(\left(\frac{1}{x - 1} + \frac{1}{1 + x}\right) - \frac{2}{x}\right)} \cdot \frac{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}\]
   0.1
9. Applied simplify to get
   \[\left(\left(\frac{1}{x - 1} + \frac{1}{1 + x}\right) - \frac{2}{x}\right) \cdot \color{red}{\frac{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}{\left(\frac{1}{x + 1} - \frac{2}{x}\right) - \frac{1}{x - 1}}} \leadsto \left(\left(\frac{1}{x - 1} + \frac{1}{1 + x}\right) - \frac{2}{x}\right) \cdot \color{blue}{1}\]
   0.1