if x < -8.724425f0

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   8.6
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
   \[\color{red}{2 \cdot \frac{1}{{x}^{5}} + \left(2 \cdot \frac{1}{{x}^{7}} + 2 \cdot \frac{1}{{x}^{3}}\right)} \leadsto \color{blue}{\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3}}\]
   0.9
5. Applied taylor to get
   \[\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3} \leadsto \left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \frac{2}{{x}^3}\]
   0.9
6. Taylor expanded around 0 to get
   \[\left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \color{red}{\frac{2}{{x}^3}} \leadsto \left(\frac{2}{{x}^{5}} + \frac{2}{{x}^{7}}\right) + \color{blue}{\frac{2}{{x}^3}}\]
   0.9
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

---

8. Applied final simplification

if -8.724425f0 < x < 13.294522f0

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 sub-neg to get
   \[\color{red}{\left(\frac{1}{x + 1} - \frac{2}{x}\right)} + \frac{1}{x - 1} \leadsto \color{blue}{\left(\frac{1}{x + 1} + \left(-\frac{2}{x}\right)\right)} + \frac{1}{x - 1}\]
   0.1
4. Applied associate-+l+ to get
   \[\color{red}{\left(\frac{1}{x + 1} + \left(-\frac{2}{x}\right)\right) + \frac{1}{x - 1}} \leadsto \color{blue}{\frac{1}{x + 1} + \left(\left(-\frac{2}{x}\right) + \frac{1}{x - 1}\right)}\]
   0.1
5. Using strategy rm
   0.1
6. Applied distribute-neg-frac to get
   \[\frac{1}{x + 1} + \left(\color{red}{\left(-\frac{2}{x}\right)} + \frac{1}{x - 1}\right) \leadsto \frac{1}{x + 1} + \left(\color{blue}{\frac{-2}{x}} + \frac{1}{x - 1}\right)\]
   0.1
7. Applied frac-add to get
   \[\frac{1}{x + 1} + \color{red}{\left(\frac{-2}{x} + \frac{1}{x - 1}\right)} \leadsto \frac{1}{x + 1} + \color{blue}{\frac{\left(-2\right) \cdot \left(x - 1\right) + x \cdot 1}{x \cdot \left(x - 1\right)}}\]
   0.1
8. Applied simplify to get
   \[\frac{1}{x + 1} + \frac{\color{red}{\left(-2\right) \cdot \left(x - 1\right) + x \cdot 1}}{x \cdot \left(x - 1\right)} \leadsto \frac{1}{x + 1} + \frac{\color{blue}{(\left(-2\right) * \left(x - 1\right) + x)_*}}{x \cdot \left(x - 1\right)}\]
   0.1

if 13.294522f0 < x

1. Started with
   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
   8.9
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