Initial program 30.0
\[\sqrt{x + 1} - \sqrt{x}\]
Initial simplification30.0
\[\leadsto \sqrt{1 + x} - \sqrt{x}\]
- Using strategy
rm Applied add-cube-cbrt30.0
\[\leadsto \sqrt{\color{blue}{\left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{1 + x}}} - \sqrt{x}\]
Applied sqrt-prod30.0
\[\leadsto \color{blue}{\sqrt{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}} \cdot \sqrt{\sqrt[3]{1 + x}}} - \sqrt{x}\]
Simplified30.0
\[\leadsto \color{blue}{\left|\sqrt[3]{x + 1}\right|} \cdot \sqrt{\sqrt[3]{1 + x}} - \sqrt{x}\]
- Using strategy
rm Applied flip--29.9
\[\leadsto \color{blue}{\frac{\left(\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}}\right) \cdot \left(\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}}\right) - \sqrt{x} \cdot \sqrt{x}}{\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}} + \sqrt{x}}}\]
- Using strategy
rm Applied expm1-log1p-u29.9
\[\leadsto \frac{\color{blue}{(e^{\log_* (1 + \left(\left(\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}}\right) \cdot \left(\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}}\right) - \sqrt{x} \cdot \sqrt{x}\right))} - 1)^*}}{\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}} + \sqrt{x}}\]
- Using strategy
rm Applied add-exp-log29.9
\[\leadsto \frac{(e^{\log_* (1 + \left(\left(\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}}\right) \cdot \left(\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\sqrt[3]{1 + x}}\right) - \sqrt{x} \cdot \sqrt{x}\right))} - 1)^*}{\left|\sqrt[3]{x + 1}\right| \cdot \sqrt{\color{blue}{e^{\log \left(\sqrt[3]{1 + x}\right)}}} + \sqrt{x}}\]
Final simplification29.9
\[\leadsto \frac{(e^{\log_* (1 + \left(\left(\sqrt{\sqrt[3]{1 + x}} \cdot \left|\sqrt[3]{1 + x}\right|\right) \cdot \left(\sqrt{\sqrt[3]{1 + x}} \cdot \left|\sqrt[3]{1 + x}\right|\right) - \sqrt{x} \cdot \sqrt{x}\right))} - 1)^*}{\left|\sqrt[3]{1 + x}\right| \cdot \sqrt{e^{\log \left(\sqrt[3]{1 + x}\right)}} + \sqrt{x}}\]
