Initial program 14.1
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
Simplified14.1
\[\leadsto \color{blue}{\frac{\frac{\pi}{b \cdot b - a \cdot a}}{\frac{2}{\frac{1}{a} - \frac{1}{b}}}}\]
- Using strategy
rm Applied frac-sub14.1
\[\leadsto \frac{\frac{\pi}{b \cdot b - a \cdot a}}{\frac{2}{\color{blue}{\frac{1 \cdot b - a \cdot 1}{a \cdot b}}}}\]
Applied associate-/r/14.1
\[\leadsto \frac{\frac{\pi}{b \cdot b - a \cdot a}}{\color{blue}{\frac{2}{1 \cdot b - a \cdot 1} \cdot \left(a \cdot b\right)}}\]
Applied difference-of-squares9.2
\[\leadsto \frac{\frac{\pi}{\color{blue}{\left(b + a\right) \cdot \left(b - a\right)}}}{\frac{2}{1 \cdot b - a \cdot 1} \cdot \left(a \cdot b\right)}\]
Applied *-un-lft-identity9.2
\[\leadsto \frac{\frac{\color{blue}{1 \cdot \pi}}{\left(b + a\right) \cdot \left(b - a\right)}}{\frac{2}{1 \cdot b - a \cdot 1} \cdot \left(a \cdot b\right)}\]
Applied times-frac8.6
\[\leadsto \frac{\color{blue}{\frac{1}{b + a} \cdot \frac{\pi}{b - a}}}{\frac{2}{1 \cdot b - a \cdot 1} \cdot \left(a \cdot b\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{\frac{1}{b + a}}{\frac{2}{1 \cdot b - a \cdot 1}} \cdot \frac{\frac{\pi}{b - a}}{a \cdot b}}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{\left(b - a\right) \cdot \frac{1}{2}}{b + a}} \cdot \frac{\frac{\pi}{b - a}}{a \cdot b}\]
- Using strategy
rm Applied clear-num0.3
\[\leadsto \color{blue}{\frac{1}{\frac{b + a}{\left(b - a\right) \cdot \frac{1}{2}}}} \cdot \frac{\frac{\pi}{b - a}}{a \cdot b}\]
Final simplification0.3
\[\leadsto \frac{\frac{\pi}{b - a}}{a \cdot b} \cdot \frac{1}{\frac{b + a}{\left(b - a\right) \cdot \frac{1}{2}}}\]
