Initial program 20.0
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
- Using strategy
rm Applied frac-sub20.0
\[\leadsto \color{blue}{\frac{1 \cdot \sqrt{x + 1} - \sqrt{x} \cdot 1}{\sqrt{x} \cdot \sqrt{x + 1}}}\]
Applied simplify20.0
\[\leadsto \frac{\color{blue}{\sqrt{x + 1} - \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Using strategy
rm Applied flip--19.7
\[\leadsto \frac{\color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
Applied associate-/l/19.7
\[\leadsto \color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\left(\sqrt{x} \cdot \sqrt{x + 1}\right) \cdot \left(\sqrt{x + 1} + \sqrt{x}\right)}}\]
- Using strategy
rm Applied associate-/r*19.7
\[\leadsto \color{blue}{\frac{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x} \cdot \sqrt{x + 1}}}{\sqrt{x + 1} + \sqrt{x}}}\]
Applied simplify0.4
\[\leadsto \frac{\color{blue}{\frac{\frac{1}{\sqrt{x}}}{\sqrt{1 + x}}}}{\sqrt{x + 1} + \sqrt{x}}\]
- Using strategy
rm Applied pow1/20.4
\[\leadsto \frac{\frac{\frac{1}{\color{blue}{{x}^{\frac{1}{2}}}}}{\sqrt{1 + x}}}{\sqrt{x + 1} + \sqrt{x}}\]
Applied pow-flip0.2
\[\leadsto \frac{\frac{\color{blue}{{x}^{\left(-\frac{1}{2}\right)}}}{\sqrt{1 + x}}}{\sqrt{x + 1} + \sqrt{x}}\]
