if x < -3.2784791869173944e-06

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   20.5
2. Applied taylor to get
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \leadsto 2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)\]
   0.6
3. Taylor expanded around inf to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
   0.6
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. Applied taylor to get
   \[\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^3}\right) + \frac{2}{{x}^{5}} \leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^3}\right) + \frac{2}{{x}^{5}}\]
   0.6
6. Taylor expanded around 0 to get
   \[\left(\frac{2}{{x}^{7}} + \color{red}{\frac{2}{{x}^3}}\right) + \frac{2}{{x}^{5}} \leadsto \left(\frac{2}{{x}^{7}} + \color{blue}{\frac{2}{{x}^3}}\right) + \frac{2}{{x}^{5}}\]
   0.6
7. Applied simplify to get
   \[\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^3}\right) + \frac{2}{{x}^{5}} \leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{x}}{x \cdot x}\]
   0.1

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8. Applied final simplification

if -3.2784791869173944e-06 < x < 501837.3637557024

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   0.2

if 501837.3637557024 < x

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   19.2
2. Applied taylor to get
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \leadsto 2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)\]
   0.4
3. Taylor expanded around inf to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)}\]
   0.4
4. Applied simplify to get
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^3}\right) + \frac{2}{{x}^{5}}}\]
   0.5