Initial program 20.4
\[\frac{\left(x - y\right) \cdot \left(x + y\right)}{x \cdot x + y \cdot y}\]
Initial simplification20.4
\[\leadsto \frac{\left(x - y\right) \cdot \left(y + x\right)}{(x \cdot x + \left(y \cdot y\right))_*}\]
- Using strategy
rm Applied add-sqr-sqrt20.4
\[\leadsto \frac{\left(x - y\right) \cdot \left(y + x\right)}{\color{blue}{\sqrt{(x \cdot x + \left(y \cdot y\right))_*} \cdot \sqrt{(x \cdot x + \left(y \cdot y\right))_*}}}\]
Applied times-frac20.4
\[\leadsto \color{blue}{\frac{x - y}{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}} \cdot \frac{y + x}{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}}\]
Simplified20.4
\[\leadsto \color{blue}{\frac{x - y}{\sqrt{x^2 + y^2}^*}} \cdot \frac{y + x}{\sqrt{(x \cdot x + \left(y \cdot y\right))_*}}\]
Simplified0.0
\[\leadsto \frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot \color{blue}{\frac{x + y}{\sqrt{x^2 + y^2}^*}}\]
- Using strategy
rm Applied associate-*r/0.0
\[\leadsto \color{blue}{\frac{\frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot \left(x + y\right)}{\sqrt{x^2 + y^2}^*}}\]
- Using strategy
rm Applied distribute-lft-in0.0
\[\leadsto \frac{\color{blue}{\frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot x + \frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot y}}{\sqrt{x^2 + y^2}^*}\]
- Using strategy
rm Applied log1p-expm1-u0.0
\[\leadsto \color{blue}{\log_* (1 + (e^{\frac{\frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot x + \frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot y}{\sqrt{x^2 + y^2}^*}} - 1)^*)}\]
Final simplification0.0
\[\leadsto \log_* (1 + (e^{\frac{\frac{x - y}{\sqrt{x^2 + y^2}^*} \cdot x + y \cdot \frac{x - y}{\sqrt{x^2 + y^2}^*}}{\sqrt{x^2 + y^2}^*}} - 1)^*)\]
