Initial program 14.8
\[\frac{x}{x \cdot x + 1}\]
Initial simplification14.8
\[\leadsto \frac{x}{(x \cdot x + 1)_*}\]
- Using strategy
rm Applied *-un-lft-identity14.8
\[\leadsto \frac{x}{\color{blue}{1 \cdot (x \cdot x + 1)_*}}\]
Applied associate-/r*14.8
\[\leadsto \color{blue}{\frac{\frac{x}{1}}{(x \cdot x + 1)_*}}\]
- Using strategy
rm Applied add-sqr-sqrt14.8
\[\leadsto \frac{\frac{x}{1}}{\color{blue}{\sqrt{(x \cdot x + 1)_*} \cdot \sqrt{(x \cdot x + 1)_*}}}\]
Applied div-inv14.8
\[\leadsto \frac{\color{blue}{x \cdot \frac{1}{1}}}{\sqrt{(x \cdot x + 1)_*} \cdot \sqrt{(x \cdot x + 1)_*}}\]
Applied times-frac14.7
\[\leadsto \color{blue}{\frac{x}{\sqrt{(x \cdot x + 1)_*}} \cdot \frac{\frac{1}{1}}{\sqrt{(x \cdot x + 1)_*}}}\]
Simplified14.7
\[\leadsto \color{blue}{\frac{x}{\sqrt{1^2 + x^2}^*}} \cdot \frac{\frac{1}{1}}{\sqrt{(x \cdot x + 1)_*}}\]
Simplified0.0
\[\leadsto \frac{x}{\sqrt{1^2 + x^2}^*} \cdot \color{blue}{\frac{1}{\sqrt{1^2 + x^2}^*}}\]
Final simplification0.0
\[\leadsto \frac{x}{\sqrt{1^2 + x^2}^*} \cdot \frac{1}{\sqrt{1^2 + x^2}^*}\]
