Initial program 14.5
\[\frac{x}{x \cdot x + 1}\]
Simplified14.5
\[\leadsto \color{blue}{\frac{x}{(x \cdot x + 1)_*}}\]
- Using strategy
rm Applied *-un-lft-identity14.5
\[\leadsto \frac{\color{blue}{1 \cdot x}}{(x \cdot x + 1)_*}\]
Applied associate-/l*14.6
\[\leadsto \color{blue}{\frac{1}{\frac{(x \cdot x + 1)_*}{x}}}\]
- Using strategy
rm Applied *-un-lft-identity14.6
\[\leadsto \frac{1}{\frac{(x \cdot x + 1)_*}{\color{blue}{1 \cdot x}}}\]
Applied add-sqr-sqrt14.6
\[\leadsto \frac{1}{\frac{\color{blue}{\sqrt{(x \cdot x + 1)_*} \cdot \sqrt{(x \cdot x + 1)_*}}}{1 \cdot x}}\]
Applied times-frac14.6
\[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{(x \cdot x + 1)_*}}{1} \cdot \frac{\sqrt{(x \cdot x + 1)_*}}{x}}}\]
Applied add-cube-cbrt14.6
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{\sqrt{(x \cdot x + 1)_*}}{1} \cdot \frac{\sqrt{(x \cdot x + 1)_*}}{x}}\]
Applied times-frac14.6
\[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt{(x \cdot x + 1)_*}}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt{(x \cdot x + 1)_*}}{x}}}\]
Simplified14.6
\[\leadsto \color{blue}{\frac{1}{\sqrt{1^2 + x^2}^*}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt{(x \cdot x + 1)_*}}{x}}\]
Simplified0.0
\[\leadsto \frac{1}{\sqrt{1^2 + x^2}^*} \cdot \color{blue}{\frac{x}{\sqrt{1^2 + x^2}^*}}\]
Final simplification0.0
\[\leadsto \frac{1}{\sqrt{1^2 + x^2}^*} \cdot \frac{x}{\sqrt{1^2 + x^2}^*}\]
