Initial program 14.3
\[\frac{1}{x + 1} - \frac{1}{x}\]
- Using strategy
rm
Applied frac-sub 13.7
\[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]
Applied simplify 13.7
\[\leadsto \frac{\color{blue}{x - \left(1 + x\right)}}{\left(x + 1\right) \cdot x}\]
- Using strategy
rm
Applied add-cube-cbrt 14.4
\[\leadsto \frac{x - \left(1 + x\right)}{\color{blue}{{\left(\sqrt[3]{\left(x + 1\right) \cdot x}\right)}^3}}\]
Applied add-cube-cbrt 14.4
\[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x - \left(1 + x\right)}\right)}^3}}{{\left(\sqrt[3]{\left(x + 1\right) \cdot x}\right)}^3}\]
Applied cube-undiv 14.5
\[\leadsto \color{blue}{{\left(\frac{\sqrt[3]{x - \left(1 + x\right)}}{\sqrt[3]{\left(x + 1\right) \cdot x}}\right)}^3}\]
Applied taylor 1.4
\[\leadsto {\left(\frac{\sqrt[3]{-1}}{\sqrt[3]{\left(x + 1\right) \cdot x}}\right)}^3\]
Taylor expanded around 0 1.4
\[\leadsto {\left(\frac{\sqrt[3]{\color{blue}{-1}}}{\sqrt[3]{\left(x + 1\right) \cdot x}}\right)}^3\]
Applied simplify 0.1
\[\leadsto \color{blue}{\frac{\frac{-1}{x}}{x + 1}}\]
- Removed slow pow expressions
