Initial program 10.1
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
Initial simplification10.1
\[\leadsto \left(\frac{1}{x - 1} + \frac{1}{x + 1}\right) - \frac{2}{x}\]
- Using strategy
rm Applied frac-add26.6
\[\leadsto \color{blue}{\frac{1 \cdot \left(x + 1\right) + \left(x - 1\right) \cdot 1}{\left(x - 1\right) \cdot \left(x + 1\right)}} - \frac{2}{x}\]
Applied frac-sub25.8
\[\leadsto \color{blue}{\frac{\left(1 \cdot \left(x + 1\right) + \left(x - 1\right) \cdot 1\right) \cdot x - \left(\left(x - 1\right) \cdot \left(x + 1\right)\right) \cdot 2}{\left(\left(x - 1\right) \cdot \left(x + 1\right)\right) \cdot x}}\]
Simplified25.8
\[\leadsto \frac{\color{blue}{\left(\left(x + 1\right) + \left(x - 1\right)\right) \cdot x - \left(x \cdot x - 1\right) \cdot 2}}{\left(\left(x - 1\right) \cdot \left(x + 1\right)\right) \cdot x}\]
Simplified25.8
\[\leadsto \frac{\left(\left(x + 1\right) + \left(x - 1\right)\right) \cdot x - \left(x \cdot x - 1\right) \cdot 2}{\color{blue}{x \cdot \left(x \cdot x - 1\right)}}\]
Taylor expanded around 0 0.3
\[\leadsto \frac{\color{blue}{2}}{x \cdot \left(x \cdot x - 1\right)}\]
Taylor expanded around 0 0.3
\[\leadsto \frac{2}{\color{blue}{{x}^{3} - x}}\]
Final simplification0.3
\[\leadsto \frac{2}{{x}^{3} - x}\]
