Initial program 19.8
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
- Using strategy
rm
Applied frac-sub 19.8
\[\leadsto \color{blue}{\frac{1 \cdot \sqrt{x + 1} - \sqrt{x} \cdot 1}{\sqrt{x} \cdot \sqrt{x + 1}}}\]
Applied simplify 19.8
\[\leadsto \frac{\color{blue}{\sqrt{1 + x} - \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Using strategy
rm
Applied flip-- 19.6
\[\leadsto \frac{\color{blue}{\frac{{\left(\sqrt{1 + x}\right)}^2 - {\left(\sqrt{x}\right)}^2}{\sqrt{1 + x} + \sqrt{x}}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
Applied simplify 0.4
\[\leadsto \frac{\frac{\color{blue}{1}}{\sqrt{1 + x} + \sqrt{x}}}{\sqrt{x} \cdot \sqrt{x + 1}}\]
- Using strategy
rm
Applied add-sqr-sqrt 0.4
\[\leadsto \frac{\frac{1}{\sqrt{1 + x} + \sqrt{x}}}{\sqrt{x} \cdot \color{blue}{{\left(\sqrt{\sqrt{x + 1}}\right)}^2}}\]
Applied add-sqr-sqrt 0.7
\[\leadsto \frac{\frac{1}{\sqrt{1 + x} + \sqrt{x}}}{\color{blue}{{\left(\sqrt{\sqrt{x}}\right)}^2} \cdot {\left(\sqrt{\sqrt{x + 1}}\right)}^2}\]
Applied square-unprod 0.7
\[\leadsto \frac{\frac{1}{\sqrt{1 + x} + \sqrt{x}}}{\color{blue}{{\left(\sqrt{\sqrt{x}} \cdot \sqrt{\sqrt{x + 1}}\right)}^2}}\]
- Removed slow pow expressions
