Initial program 20.0
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
- Using strategy
rm Applied flip--20.0
\[\leadsto \color{blue}{\frac{\frac{1}{\sqrt{x}} \cdot \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \cdot \frac{1}{\sqrt{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}}\]
Applied simplify20.0
\[\leadsto \frac{\color{blue}{\frac{1}{x} - \frac{1}{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
- Using strategy
rm Applied frac-sub19.4
\[\leadsto \frac{\color{blue}{\frac{1 \cdot \left(x + 1\right) - x \cdot 1}{x \cdot \left(x + 1\right)}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
Applied simplify5.6
\[\leadsto \frac{\frac{\color{blue}{1}}{x \cdot \left(x + 1\right)}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
Applied simplify5.6
\[\leadsto \frac{\frac{1}{\color{blue}{(x \cdot x + x)_*}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
- Using strategy
rm Applied *-un-lft-identity5.6
\[\leadsto \frac{\frac{1}{(x \cdot x + x)_*}}{\color{blue}{1 \cdot \left(\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}\right)}}\]
Applied add-sqr-sqrt5.7
\[\leadsto \frac{\color{blue}{\sqrt{\frac{1}{(x \cdot x + x)_*}} \cdot \sqrt{\frac{1}{(x \cdot x + x)_*}}}}{1 \cdot \left(\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}\right)}\]
Applied times-frac5.6
\[\leadsto \color{blue}{\frac{\sqrt{\frac{1}{(x \cdot x + x)_*}}}{1} \cdot \frac{\sqrt{\frac{1}{(x \cdot x + x)_*}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}}\]
Applied simplify5.6
\[\leadsto \color{blue}{\sqrt{\frac{1}{(x \cdot x + x)_*}}} \cdot \frac{\sqrt{\frac{1}{(x \cdot x + x)_*}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
