if x < -1.5245538f0

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   8.2
2. Using strategy rm
   8.2
3. Applied frac-sub to get
   \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right)} + \frac{1}{x - 1} \leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
   23.2
4. Applied frac-add to get
   \[\color{red}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}} \leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\]
   22.9
5. Applied simplify to get
   \[\frac{\color{red}{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)} \leadsto \frac{\color{blue}{(\left(x - 1\right) * \left(x - (2 * x + 2)_*\right) + \left(x \cdot x + x\right))_*}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
   23.9
6. Applied simplify to get
   \[\frac{(\left(x - 1\right) * \left(x - (2 * x + 2)_*\right) + \left(x \cdot x + x\right))_*}{\color{red}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}} \leadsto \frac{(\left(x - 1\right) * \left(x - (2 * x + 2)_*\right) + \left(x \cdot x + x\right))_*}{\color{blue}{\left(x - 1\right) \cdot (x * x + x)_*}}\]
   28.1
7. Applied taylor to get
   \[\frac{(\left(x - 1\right) * \left(x - (2 * x + 2)_*\right) + \left(x \cdot x + x\right))_*}{\left(x - 1\right) \cdot (x * x + x)_*} \leadsto \frac{(\left(\frac{1}{x} - 1\right) * \left(\frac{1}{x} - (2 * \left(\frac{1}{x}\right) + 2)_*\right) + \left(\frac{1}{{x}^2} + \frac{1}{x}\right))_*}{\left(x - 1\right) \cdot (x * x + x)_*}\]
   0.1
8. Taylor expanded around inf to get
   \[\frac{\color{red}{(\left(\frac{1}{x} - 1\right) * \left(\frac{1}{x} - (2 * \left(\frac{1}{x}\right) + 2)_*\right) + \left(\frac{1}{{x}^2} + \frac{1}{x}\right))_*}}{\left(x - 1\right) \cdot (x * x + x)_*} \leadsto \frac{\color{blue}{(\left(\frac{1}{x} - 1\right) * \left(\frac{1}{x} - (2 * \left(\frac{1}{x}\right) + 2)_*\right) + \left(\frac{1}{{x}^2} + \frac{1}{x}\right))_*}}{\left(x - 1\right) \cdot (x * x + x)_*}\]
   0.1
9. Applied simplify to get
   \[\frac{(\left(\frac{1}{x} - 1\right) * \left(\frac{1}{x} - (2 * \left(\frac{1}{x}\right) + 2)_*\right) + \left(\frac{1}{{x}^2} + \frac{1}{x}\right))_*}{\left(x - 1\right) \cdot (x * x + x)_*} \leadsto \frac{(\left(\frac{1}{x} - 1\right) * \left(\frac{1}{x} - (2 * \left(\frac{1}{x}\right) + 2)_*\right) + \left(\frac{1}{x} + \frac{\frac{1}{x}}{x}\right))_*}{\left(x - 1\right) \cdot (x * x + x)_*}\]
   0.1

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10. Applied final simplification

if -1.5245538f0 < x < 12.483333f0

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

if 12.483333f0 < 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
5. Applied taylor to get
   \[\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3} \leadsto \left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3}\]
   0.8
6. Taylor expanded around 0 to get
   \[\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \color{red}{\frac{2}{{x}^3}} \leadsto \left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \color{blue}{\frac{2}{{x}^3}}\]
   0.8
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