Initial program 29.8
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
- Using strategy
rm
Applied flip3-- 29.7
\[\leadsto \color{blue}{\frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^{3} - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^{3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}}\]
Applied simplify 29.7
\[\leadsto \frac{\color{blue}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + \left({\left({x}^{\left(\frac{1}{3}\right)}\right)}^2 + {\left(x + 1\right)}^{\left(\frac{1}{3}\right)} \cdot {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied simplify 29.7
\[\leadsto \frac{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^3 - {\left({x}^{\left(\frac{1}{3}\right)}\right)}^3}{\color{blue}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}}\]
Applied taylor 29.7
\[\leadsto \frac{{\left({\left(1 + x\right)}^{\frac{1}{3}}\right)}^3 - {\left({x}^{\frac{1}{3}}\right)}^3}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
Taylor expanded around 0 29.7
\[\leadsto \frac{\color{blue}{{\left({\left(1 + x\right)}^{\frac{1}{3}}\right)}^3 - {\left({x}^{\frac{1}{3}}\right)}^3}}{{\left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right)}^2 + {x}^{\left(\frac{1}{3}\right)} \cdot \left({\left(x + 1\right)}^{\left(\frac{1}{3}\right)} + {x}^{\left(\frac{1}{3}\right)}\right)}\]
Applied simplify 3.1
\[\leadsto \color{blue}{\frac{1}{{\left(1 + x\right)}^{\left(\frac{1}{3}\right)} \cdot \left({x}^{\left(\frac{1}{3}\right)} + {\left(1 + x\right)}^{\left(\frac{1}{3}\right)}\right) + {\left({x}^{\left(\frac{1}{3}\right)}\right)}^2}}\]
- Removed slow pow expressions
