if x < -0.01639637f0 or 17.42791f0 < x

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   9.1
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
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3}}\]
   0.7
5. Applied taylor to get
   \[\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3} \leadsto \left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3}\]
   0.7
6. Taylor expanded around 0 to get
   \[\left(\frac{2}{{x}^{5}} + \color{red}{\frac{2}{{x}^{7}}}\right) + \frac{2}{{x}^3} \leadsto \left(\frac{2}{{x}^{5}} + \color{blue}{\frac{2}{{x}^{7}}}\right) + \frac{2}{{x}^3}\]
   0.7
7. Applied simplify to get
   \[\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3} \leadsto \frac{\frac{2}{x}}{x \cdot x} + \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right)\]
   0.1

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8. Applied final simplification

if -0.01639637f0 < x < 17.42791f0

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 frac-sub to get
   \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right)} + \frac{1}{x - 1} \leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
   0.1
4. Applied simplify to get
   \[\frac{\color{red}{1 \cdot x - \left(x + 1\right) \cdot 2}}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1} \leadsto \frac{\color{blue}{x - (2 * x + 2)_*}}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}\]
   0.1
5. Applied simplify to get
   \[\frac{x - (2 * x + 2)_*}{\color{red}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1} \leadsto \frac{x - (2 * x + 2)_*}{\color{blue}{(x * x + x)_*}} + \frac{1}{x - 1}\]
   0.1