Initial program 20.2
\[\frac{\left(x - y\right) \cdot \left(x + y\right)}{x \cdot x + y \cdot y}\]
Simplified20.2
\[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot \left(y + x\right)}{(x \cdot x + \left(y \cdot y\right))_*}}\]
- Using strategy
rm Applied clear-num20.2
\[\leadsto \color{blue}{\frac{1}{\frac{(x \cdot x + \left(y \cdot y\right))_*}{\left(x - y\right) \cdot \left(y + x\right)}}}\]
- Using strategy
rm Applied add-sqr-sqrt20.2
\[\leadsto \frac{1}{\frac{\color{blue}{\sqrt{(x \cdot x + \left(y \cdot y\right))_*} \cdot \sqrt{(x \cdot x + \left(y \cdot y\right))_*}}}{\left(x - y\right) \cdot \left(y + x\right)}}\]
Applied times-frac20.2
\[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}{x - y} \cdot \frac{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}{y + x}}}\]
Applied add-cube-cbrt20.2
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}{x - y} \cdot \frac{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}{y + x}}\]
Applied times-frac20.2
\[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}{x - y}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}{y + x}}}\]
Simplified20.2
\[\leadsto \color{blue}{\frac{x - y}{\sqrt{x^2 + y^2}^*}} \cdot \frac{\sqrt[3]{1}}{\frac{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}{y + x}}\]
Simplified0.0
\[\leadsto \frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot \color{blue}{\frac{y + x}{\sqrt{y^2 + x^2}^*}}\]
Final simplification0.0
\[\leadsto \frac{y + x}{\sqrt{y^2 + x^2}^*} \cdot \frac{x - y}{\sqrt{x^2 + y^2}^*}\]
