Initial program 9.7
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
Initial simplification9.7
\[\leadsto \frac{1}{x + 1} + \left(\frac{1}{x - 1} - \frac{2}{x}\right)\]
- Using strategy
rm Applied +-commutative9.7
\[\leadsto \color{blue}{\left(\frac{1}{x - 1} - \frac{2}{x}\right) + \frac{1}{x + 1}}\]
- Using strategy
rm Applied frac-sub25.6
\[\leadsto \color{blue}{\frac{1 \cdot x - \left(x - 1\right) \cdot 2}{\left(x - 1\right) \cdot x}} + \frac{1}{x + 1}\]
Applied frac-add24.8
\[\leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x - 1\right) \cdot 2\right) \cdot \left(x + 1\right) + \left(\left(x - 1\right) \cdot x\right) \cdot 1}{\left(\left(x - 1\right) \cdot x\right) \cdot \left(x + 1\right)}}\]
Simplified25.3
\[\leadsto \frac{\color{blue}{(\left((\left(x - 1\right) \cdot \left(-2\right) + x)_*\right) \cdot \left(x + 1\right) + \left(\left(x - 1\right) \cdot x\right))_*}}{\left(\left(x - 1\right) \cdot x\right) \cdot \left(x + 1\right)}\]
Simplified25.3
\[\leadsto \frac{(\left((\left(x - 1\right) \cdot \left(-2\right) + x)_*\right) \cdot \left(x + 1\right) + \left(\left(x - 1\right) \cdot x\right))_*}{\color{blue}{\left(x - 1\right) \cdot (x \cdot x + x)_*}}\]
Taylor expanded around 0 0.3
\[\leadsto \frac{\color{blue}{2}}{\left(x - 1\right) \cdot (x \cdot x + x)_*}\]
Taylor expanded around inf 0.3
\[\leadsto \frac{2}{\color{blue}{{x}^{3} - x}}\]
Final simplification0.3
\[\leadsto \frac{2}{{x}^{3} - x}\]
