Initial program 19.7
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
- Using strategy
rm Applied frac-sub19.7
\[\leadsto \color{blue}{\frac{1 \cdot \sqrt{x + 1} - \sqrt{x} \cdot 1}{\sqrt{x} \cdot \sqrt{x + 1}}}\]
Applied simplify19.7
\[\leadsto \frac{\color{blue}{\sqrt{x + 1} - \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Using strategy
rm Applied flip--19.4
\[\leadsto \frac{\color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
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-sqr-sqrt0.6
\[\leadsto \color{blue}{\sqrt{\frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}} \cdot \sqrt{\frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}}}\]
Applied simplify0.9
\[\leadsto \color{blue}{\sqrt{\frac{1}{(\left(\sqrt{x + 1}\right) \cdot x + \left(\left(x + 1\right) \cdot \sqrt{x}\right))_*}}} \cdot \sqrt{\frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}}\]
Applied simplify0.9
\[\leadsto \sqrt{\frac{1}{(\left(\sqrt{x + 1}\right) \cdot x + \left(\left(x + 1\right) \cdot \sqrt{x}\right))_*}} \cdot \color{blue}{\sqrt{\frac{1}{(\left(\sqrt{x + 1}\right) \cdot x + \left(\left(x + 1\right) \cdot \sqrt{x}\right))_*}}}\]
