Initial program 9.8
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
- Using strategy
rm Applied frac-sub25.9
\[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
Applied frac-add25.2
\[\leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\]
Simplified25.6
\[\leadsto \frac{\color{blue}{(\left(x - (x \cdot 2 + 2)_*\right) \cdot \left(x - 1\right) + \left((x \cdot x + x)_*\right))_*}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
Simplified25.6
\[\leadsto \frac{(\left(x - (x \cdot 2 + 2)_*\right) \cdot \left(x - 1\right) + \left((x \cdot x + x)_*\right))_*}{\color{blue}{(x \cdot x + -1)_* \cdot x}}\]
Taylor expanded around inf 0.3
\[\leadsto \frac{\color{blue}{2}}{(x \cdot x + -1)_* \cdot x}\]
Final simplification0.3
\[\leadsto \frac{2}{(x \cdot x + -1)_* \cdot x}\]
