Initial program 14.2
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
- Using strategy
rm Applied frac-sub14.2
\[\leadsto \left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \color{blue}{\frac{1 \cdot b - a \cdot 1}{a \cdot b}}\]
Applied associate-*l/14.2
\[\leadsto \color{blue}{\frac{\pi \cdot \frac{1}{b \cdot b - a \cdot a}}{2}} \cdot \frac{1 \cdot b - a \cdot 1}{a \cdot b}\]
Applied frac-times14.2
\[\leadsto \color{blue}{\frac{\left(\pi \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(1 \cdot b - a \cdot 1\right)}{2 \cdot \left(a \cdot b\right)}}\]
Simplified0.2
\[\leadsto \frac{\color{blue}{\frac{\pi}{b + a}}}{2 \cdot \left(a \cdot b\right)}\]
- Using strategy
rm Applied div-inv0.3
\[\leadsto \color{blue}{\frac{\pi}{b + a} \cdot \frac{1}{2 \cdot \left(a \cdot b\right)}}\]
Final simplification0.3
\[\leadsto \frac{\pi}{b + a} \cdot \frac{1}{\left(a \cdot b\right) \cdot 2}\]
