Initial program 14.2
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
Initial simplification9.5
\[\leadsto \frac{(\left(\frac{\pi}{2}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{2}}{a}\right))_*}{\left(a + b\right) \cdot \left(b - a\right)}\]
- Using strategy
rm Applied *-un-lft-identity9.5
\[\leadsto \frac{\color{blue}{1 \cdot (\left(\frac{\pi}{2}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{2}}{a}\right))_*}}{\left(a + b\right) \cdot \left(b - a\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{1}{a + b} \cdot \frac{(\left(\frac{\pi}{2}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{2}}{a}\right))_*}{b - a}}\]
Simplified0.3
\[\leadsto \frac{1}{a + b} \cdot \color{blue}{\frac{\frac{\pi}{a \cdot 2} - \frac{\pi}{2 \cdot b}}{b - a}}\]
- Using strategy
rm Applied *-un-lft-identity0.3
\[\leadsto \frac{1}{a + b} \cdot \frac{\frac{\pi}{a \cdot 2} - \frac{\pi}{2 \cdot b}}{\color{blue}{1 \cdot \left(b - a\right)}}\]
Applied div-inv0.3
\[\leadsto \frac{1}{a + b} \cdot \frac{\frac{\pi}{a \cdot 2} - \color{blue}{\pi \cdot \frac{1}{2 \cdot b}}}{1 \cdot \left(b - a\right)}\]
Applied div-inv0.3
\[\leadsto \frac{1}{a + b} \cdot \frac{\color{blue}{\pi \cdot \frac{1}{a \cdot 2}} - \pi \cdot \frac{1}{2 \cdot b}}{1 \cdot \left(b - a\right)}\]
Applied distribute-lft-out--0.3
\[\leadsto \frac{1}{a + b} \cdot \frac{\color{blue}{\pi \cdot \left(\frac{1}{a \cdot 2} - \frac{1}{2 \cdot b}\right)}}{1 \cdot \left(b - a\right)}\]
Applied times-frac0.3
\[\leadsto \frac{1}{a + b} \cdot \color{blue}{\left(\frac{\pi}{1} \cdot \frac{\frac{1}{a \cdot 2} - \frac{1}{2 \cdot b}}{b - a}\right)}\]
Applied associate-*r*0.3
\[\leadsto \color{blue}{\left(\frac{1}{a + b} \cdot \frac{\pi}{1}\right) \cdot \frac{\frac{1}{a \cdot 2} - \frac{1}{2 \cdot b}}{b - a}}\]
Simplified0.3
\[\leadsto \left(\frac{1}{a + b} \cdot \frac{\pi}{1}\right) \cdot \color{blue}{\frac{\frac{1}{2 \cdot a} - \frac{\frac{1}{2}}{b}}{b - a}}\]
- Using strategy
rm Applied associate-*r/0.3
\[\leadsto \color{blue}{\frac{\frac{1}{a + b} \cdot \pi}{1}} \cdot \frac{\frac{1}{2 \cdot a} - \frac{\frac{1}{2}}{b}}{b - a}\]
Applied associate-*l/0.3
\[\leadsto \color{blue}{\frac{\left(\frac{1}{a + b} \cdot \pi\right) \cdot \frac{\frac{1}{2 \cdot a} - \frac{\frac{1}{2}}{b}}{b - a}}{1}}\]
Simplified0.3
\[\leadsto \frac{\color{blue}{\frac{\frac{\frac{1}{2}}{a} - \frac{\frac{1}{2}}{b}}{a + b} \cdot \frac{\pi}{b - a}}}{1}\]
Final simplification0.3
\[\leadsto \frac{\frac{\frac{1}{2}}{a} - \frac{\frac{1}{2}}{b}}{a + b} \cdot \frac{\pi}{b - a}\]
