Initial program 10.1
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
- Using strategy
rm Applied frac-sub26.3
\[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 2}{\left(x + 1\right) \cdot x}} + \frac{1}{x - 1}\]
Simplified26.3
\[\leadsto \frac{\color{blue}{(-1 \cdot x + -2)_*}}{\left(x + 1\right) \cdot x} + \frac{1}{x - 1}\]
Simplified26.3
\[\leadsto \frac{(-1 \cdot x + -2)_*}{\color{blue}{(x \cdot x + x)_*}} + \frac{1}{x - 1}\]
- Using strategy
rm Applied frac-add25.5
\[\leadsto \color{blue}{\frac{(-1 \cdot x + -2)_* \cdot \left(x - 1\right) + (x \cdot x + x)_* \cdot 1}{(x \cdot x + x)_* \cdot \left(x - 1\right)}}\]
Simplified25.5
\[\leadsto \frac{\color{blue}{\left(\left(x \cdot x - x\right) + 2\right) - \left(x \cdot x - x\right)}}{(x \cdot x + x)_* \cdot \left(x - 1\right)}\]
Taylor expanded around inf 0.3
\[\leadsto \frac{\color{blue}{2}}{(x \cdot x + x)_* \cdot \left(x - 1\right)}\]
- Using strategy
rm Applied associate-/r*0.1
\[\leadsto \color{blue}{\frac{\frac{2}{(x \cdot x + x)_*}}{x - 1}}\]
Final simplification0.1
\[\leadsto \frac{\frac{2}{(x \cdot x + x)_*}}{x - 1}\]
