Initial program 9.5
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
- Using strategy
rm
Applied frac-sub 26.1
\[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
Applied frac-add 25.4
\[\leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\]
Applied simplify 25.5
\[\leadsto \frac{\color{blue}{\left(\left(x - 2\right) - \left(x + x\right)\right) \cdot \left(x - 1\right) + \left(x + x \cdot x\right)}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
Applied taylor 25.4
\[\leadsto \frac{\left(2 - \left(x + {x}^2\right)\right) + \left(x + x \cdot x\right)}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
Taylor expanded around 0 25.4
\[\leadsto \frac{\color{blue}{\left(2 - \left(x + {x}^2\right)\right)} + \left(x + x \cdot x\right)}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
Applied simplify 0.1
\[\leadsto \color{blue}{\frac{\frac{\frac{2}{x}}{1 + x}}{x - 1}}\]
- Using strategy
rm
Applied *-un-lft-identity 0.1
\[\leadsto \frac{\frac{\frac{2}{x}}{1 + x}}{\color{blue}{1 \cdot \left(x - 1\right)}}\]
Applied flip-+ 0.1
\[\leadsto \frac{\frac{\frac{2}{x}}{\color{blue}{\frac{{1}^2 - {x}^2}{1 - x}}}}{1 \cdot \left(x - 1\right)}\]
Applied associate-/r/ 0.1
\[\leadsto \frac{\color{blue}{\frac{\frac{2}{x}}{{1}^2 - {x}^2} \cdot \left(1 - x\right)}}{1 \cdot \left(x - 1\right)}\]
Applied times-frac 0.1
\[\leadsto \color{blue}{\frac{\frac{\frac{2}{x}}{{1}^2 - {x}^2}}{1} \cdot \frac{1 - x}{x - 1}}\]
Applied simplify 0.1
\[\leadsto \color{blue}{\frac{\frac{2}{x}}{1 - {x}^2}} \cdot \frac{1 - x}{x - 1}\]
- Removed slow pow expressions
