Initial program 29.8
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
- Using strategy
rm Applied flip3--29.7
\[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x + 1}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}}\]
Applied simplify0.5
\[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]
Applied simplify0.5
\[\leadsto \frac{1}{\color{blue}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{x}}}\]
- Using strategy
rm Applied add-cube-cbrt0.6
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{1 + x}}} + \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{x}}\]
Applied cbrt-prod0.6
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}} \cdot \sqrt[3]{\sqrt[3]{1 + x}}\right)} + \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{x}}\]
Applied associate-*r*0.6
\[\leadsto \frac{1}{\color{blue}{\left(\sqrt[3]{1 + x} \cdot \sqrt[3]{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}\right) \cdot \sqrt[3]{\sqrt[3]{1 + x}}} + \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{x}}\]
- Using strategy
rm Applied add-cube-cbrt0.6
\[\leadsto \frac{1}{\left(\sqrt[3]{1 + x} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}} \cdot \sqrt[3]{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}\right) \cdot \sqrt[3]{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}}}\right) \cdot \sqrt[3]{\sqrt[3]{1 + x}} + \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{x}}\]
