Initial program 9.8
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
- Using strategy
rm
Applied frac-sub 25.7
\[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
Applied frac-add 25.1
\[\leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\]
Applied simplify 25.2
\[\leadsto \frac{\color{blue}{\left(x - 1\right) \cdot \left(\left(x - 2\right) - \left(x + x\right)\right) + \left(x \cdot x + x\right)}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
Applied taylor 25.1
\[\leadsto \frac{\left(2 - \left({x}^2 + x\right)\right) + \left(x \cdot x + x\right)}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
Taylor expanded around 0 25.1
\[\leadsto \frac{\color{blue}{\left(2 - \left({x}^2 + x\right)\right)} + \left(x \cdot x + x\right)}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
Applied simplify 0.1
\[\leadsto \color{blue}{\frac{\frac{2}{1 + x}}{\left(x - 1\right) \cdot x}}\]
- Removed slow pow expressions
