Initial program 30.1
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
- Using strategy
rm Applied flip3--30.1
\[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x + 1}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}}\]
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 flip3-+0.6
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{3} + {\left(\sqrt[3]{1 + x}\right)}^{3}}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} - \sqrt[3]{x} \cdot \sqrt[3]{1 + x}\right)}} \cdot \sqrt[3]{x}}\]
Applied associate-*l/8.1
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \color{blue}{\frac{\left({\left(\sqrt[3]{x}\right)}^{3} + {\left(\sqrt[3]{1 + x}\right)}^{3}\right) \cdot \sqrt[3]{x}}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} - \sqrt[3]{x} \cdot \sqrt[3]{1 + x}\right)}}}\]
Applied simplify7.9
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \frac{\color{blue}{\sqrt[3]{x} + \sqrt[3]{x} \cdot \left(x + x\right)}}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} - \sqrt[3]{x} \cdot \sqrt[3]{1 + x}\right)}}\]
- Using strategy
rm Applied add-cube-cbrt8.1
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \color{blue}{\left(\sqrt[3]{\frac{\sqrt[3]{x} + \sqrt[3]{x} \cdot \left(x + x\right)}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} - \sqrt[3]{x} \cdot \sqrt[3]{1 + x}\right)}} \cdot \sqrt[3]{\frac{\sqrt[3]{x} + \sqrt[3]{x} \cdot \left(x + x\right)}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} - \sqrt[3]{x} \cdot \sqrt[3]{1 + x}\right)}}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{x} + \sqrt[3]{x} \cdot \left(x + x\right)}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} - \sqrt[3]{x} \cdot \sqrt[3]{1 + x}\right)}}}}\]
Applied simplify8.1
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \color{blue}{\left(\sqrt[3]{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - \frac{\sqrt[3]{1 + x} - \sqrt[3]{x}}{1}}} \cdot \sqrt[3]{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - \frac{\sqrt[3]{1 + x} - \sqrt[3]{x}}{1}}}\right)} \cdot \sqrt[3]{\frac{\sqrt[3]{x} + \sqrt[3]{x} \cdot \left(x + x\right)}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} - \sqrt[3]{x} \cdot \sqrt[3]{1 + x}\right)}}}\]
Applied simplify0.6
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - \frac{\sqrt[3]{1 + x} - \sqrt[3]{x}}{1}}} \cdot \sqrt[3]{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - \frac{\sqrt[3]{1 + x} - \sqrt[3]{x}}{1}}}\right) \cdot \color{blue}{\sqrt[3]{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - 1 \cdot \left(\sqrt[3]{1 + x} - \sqrt[3]{x}\right)}}}}\]
Applied simplify0.6
\[\leadsto \frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - \frac{\sqrt[3]{1 + x} - \sqrt[3]{x}}{1}}} \cdot \sqrt[3]{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - \frac{\sqrt[3]{1 + x} - \sqrt[3]{x}}{1}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{x + \left(1 + x\right)}{\frac{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}{\sqrt[3]{x}} - \left(\sqrt[3]{1 + x} - \sqrt[3]{x}\right)}}}}\]
