Initial program 10.0
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
- Using strategy
rm Applied frac-sub25.8
\[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
Applied frac-add25.1
\[\leadsto \color{blue}{\frac{\left(1 \cdot x - \left(x + 1\right) \cdot 2\right) \cdot \left(x - 1\right) + \left(\left(x + 1\right) \cdot x\right) \cdot 1}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}}\]
Taylor expanded around 0 0.3
\[\leadsto \frac{\color{blue}{2}}{\left(\left(x + 1\right) \cdot x\right) \cdot \left(x - 1\right)}\]
- Using strategy
rm Applied associate-/r*0.1
\[\leadsto \color{blue}{\frac{\frac{2}{\left(x + 1\right) \cdot x}}{x - 1}}\]
- Using strategy
rm Applied *-un-lft-identity0.1
\[\leadsto \frac{\frac{2}{\left(x + 1\right) \cdot x}}{\color{blue}{1 \cdot \left(x - 1\right)}}\]
Applied flip-+0.1
\[\leadsto \frac{\frac{2}{\color{blue}{\frac{x \cdot x - 1 \cdot 1}{x - 1}} \cdot x}}{1 \cdot \left(x - 1\right)}\]
Applied associate-*l/0.3
\[\leadsto \frac{\frac{2}{\color{blue}{\frac{\left(x \cdot x - 1 \cdot 1\right) \cdot x}{x - 1}}}}{1 \cdot \left(x - 1\right)}\]
Applied associate-/r/0.3
\[\leadsto \frac{\color{blue}{\frac{2}{\left(x \cdot x - 1 \cdot 1\right) \cdot x} \cdot \left(x - 1\right)}}{1 \cdot \left(x - 1\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{\frac{2}{\left(x \cdot x - 1 \cdot 1\right) \cdot x}}{1} \cdot \frac{x - 1}{x - 1}}\]
Simplified0.1
\[\leadsto \color{blue}{\frac{\frac{2}{x}}{-1 + x \cdot x}} \cdot \frac{x - 1}{x - 1}\]
Simplified0.1
\[\leadsto \frac{\frac{2}{x}}{-1 + x \cdot x} \cdot \color{blue}{1}\]
Final simplification0.1
\[\leadsto \frac{\frac{2}{x}}{-1 + x \cdot x}\]
