if x < -1.128700823931291e-06 or 8727.195470384844 < x

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   20.0
2. Applied taylor to get
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \leadsto 2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)\]
   0.5
3. Taylor expanded around inf to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
   0.5
4. Applied simplify to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^3}\right) + \frac{2}{{x}^{5}}}\]
   0.6
5. Using strategy rm
   0.6
6. Applied cube-mult to get
   \[\left(\frac{2}{{x}^{7}} + \frac{2}{\color{red}{{x}^3}}\right) + \frac{2}{{x}^{5}} \leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{\color{blue}{x \cdot \left(x \cdot x\right)}}\right) + \frac{2}{{x}^{5}}\]
   0.6
7. Applied associate-/r* to get
   \[\left(\frac{2}{{x}^{7}} + \color{red}{\frac{2}{x \cdot \left(x \cdot x\right)}}\right) + \frac{2}{{x}^{5}} \leadsto \left(\frac{2}{{x}^{7}} + \color{blue}{\frac{\frac{2}{x}}{x \cdot x}}\right) + \frac{2}{{x}^{5}}\]
   0.1

if -1.128700823931291e-06 < x < 8727.195470384844

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   0.1