Initial program 15.4
\[\frac{x}{x \cdot x + 1}\]
Initial simplification15.4
\[\leadsto \frac{x}{(x \cdot x + 1)_*}\]
- Using strategy
rm Applied add-sqr-sqrt15.4
\[\leadsto \frac{x}{\color{blue}{\sqrt{(x \cdot x + 1)_*} \cdot \sqrt{(x \cdot x + 1)_*}}}\]
Applied associate-/r*15.4
\[\leadsto \color{blue}{\frac{\frac{x}{\sqrt{(x \cdot x + 1)_*}}}{\sqrt{(x \cdot x + 1)_*}}}\]
- Using strategy
rm Applied *-un-lft-identity15.4
\[\leadsto \frac{\frac{x}{\sqrt{(x \cdot x + 1)_*}}}{\color{blue}{1 \cdot \sqrt{(x \cdot x + 1)_*}}}\]
Applied add-cube-cbrt16.1
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{x}{\sqrt{(x \cdot x + 1)_*}}} \cdot \sqrt[3]{\frac{x}{\sqrt{(x \cdot x + 1)_*}}}\right) \cdot \sqrt[3]{\frac{x}{\sqrt{(x \cdot x + 1)_*}}}}}{1 \cdot \sqrt{(x \cdot x + 1)_*}}\]
Applied times-frac16.1
\[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{x}{\sqrt{(x \cdot x + 1)_*}}} \cdot \sqrt[3]{\frac{x}{\sqrt{(x \cdot x + 1)_*}}}}{1} \cdot \frac{\sqrt[3]{\frac{x}{\sqrt{(x \cdot x + 1)_*}}}}{\sqrt{(x \cdot x + 1)_*}}}\]
Simplified16.1
\[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}} \cdot \sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}}\right)} \cdot \frac{\sqrt[3]{\frac{x}{\sqrt{(x \cdot x + 1)_*}}}}{\sqrt{(x \cdot x + 1)_*}}\]
Simplified0.7
\[\leadsto \left(\sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}} \cdot \sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}}\right) \cdot \color{blue}{\frac{\sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}}}{\sqrt{1^2 + x^2}^*}}\]
Final simplification0.7
\[\leadsto \left(\sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}} \cdot \sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}}\right) \cdot \frac{\sqrt[3]{\frac{x}{\sqrt{1^2 + x^2}^*}}}{\sqrt{1^2 + x^2}^*}\]
