Initial program 19.7
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
- Using strategy
rm Applied frac-sub19.6
\[\leadsto \color{blue}{\frac{1 \cdot \sqrt{x + 1} - \sqrt{x} \cdot 1}{\sqrt{x} \cdot \sqrt{x + 1}}}\]
Applied simplify19.6
\[\leadsto \frac{\color{blue}{\sqrt{x + 1} - \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Using strategy
rm Applied flip--19.5
\[\leadsto \frac{\color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
Applied simplify0.4
\[\leadsto \frac{\frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Using strategy
rm Applied add-cbrt-cube0.5
\[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\frac{1}{\sqrt{x + 1} + \sqrt{x}} \cdot \frac{1}{\sqrt{x + 1} + \sqrt{x}}\right) \cdot \frac{1}{\sqrt{x + 1} + \sqrt{x}}}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
Applied simplify0.5
\[\leadsto \frac{\sqrt[3]{\color{blue}{\frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot \left(\sqrt{x + 1} + \sqrt{x}\right)}}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Using strategy
rm Applied add-sqr-sqrt0.5
\[\leadsto \frac{\sqrt[3]{\color{blue}{\sqrt{\frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot \left(\sqrt{x + 1} + \sqrt{x}\right)}} \cdot \sqrt{\frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot \left(\sqrt{x + 1} + \sqrt{x}\right)}}}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Removed slow
pow expressions. Applied simplify0.5
\[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{\left(\sqrt{x + 1} + \sqrt{x}\right) \cdot \left(\sqrt{x + 1} + \sqrt{x}\right)}}}{\sqrt{x + 1} \cdot \sqrt{x}}}\]
