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
\[\leadsto \color{blue}{\frac{(\left(\frac{\pi}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{b \cdot b - a \cdot a}}{a}\right))_*}{2}}\]
- Using strategy
rm Applied *-un-lft-identity14.1
\[\leadsto \frac{(\left(\frac{\pi}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{b \cdot b - a \cdot a}}{\color{blue}{1 \cdot a}}\right))_*}{2}\]
Applied difference-of-squares14.1
\[\leadsto \frac{(\left(\frac{\pi}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{\color{blue}{\left(b + a\right) \cdot \left(b - a\right)}}}{1 \cdot a}\right))_*}{2}\]
Applied *-un-lft-identity14.1
\[\leadsto \frac{(\left(\frac{\pi}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\color{blue}{1 \cdot \pi}}{\left(b + a\right) \cdot \left(b - a\right)}}{1 \cdot a}\right))_*}{2}\]
Applied times-frac13.9
\[\leadsto \frac{(\left(\frac{\pi}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\color{blue}{\frac{1}{b + a} \cdot \frac{\pi}{b - a}}}{1 \cdot a}\right))_*}{2}\]
Applied times-frac9.4
\[\leadsto \frac{(\left(\frac{\pi}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{-1}{b}\right) + \color{blue}{\left(\frac{\frac{1}{b + a}}{1} \cdot \frac{\frac{\pi}{b - a}}{a}\right)})_*}{2}\]
Simplified9.4
\[\leadsto \frac{(\left(\frac{\pi}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{-1}{b}\right) + \left(\color{blue}{\frac{1}{b + a}} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
- Using strategy
rm Applied difference-of-squares5.0
\[\leadsto \frac{(\left(\frac{\pi}{\color{blue}{\left(b + a\right) \cdot \left(b - a\right)}}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
Applied *-un-lft-identity5.0
\[\leadsto \frac{(\left(\frac{\color{blue}{1 \cdot \pi}}{\left(b + a\right) \cdot \left(b - a\right)}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
Applied times-frac4.7
\[\leadsto \frac{(\color{blue}{\left(\frac{1}{b + a} \cdot \frac{\pi}{b - a}\right)} \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
- Using strategy
rm Applied clear-num4.8
\[\leadsto \frac{(\left(\frac{1}{b + a} \cdot \color{blue}{\frac{1}{\frac{b - a}{\pi}}}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
- Using strategy
rm Applied div-inv4.8
\[\leadsto \frac{(\left(\frac{1}{b + a} \cdot \frac{1}{\color{blue}{\left(b - a\right) \cdot \frac{1}{\pi}}}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
Applied *-un-lft-identity4.8
\[\leadsto \frac{(\left(\frac{1}{b + a} \cdot \frac{\color{blue}{1 \cdot 1}}{\left(b - a\right) \cdot \frac{1}{\pi}}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
Applied times-frac4.8
\[\leadsto \frac{(\left(\frac{1}{b + a} \cdot \color{blue}{\left(\frac{1}{b - a} \cdot \frac{1}{\frac{1}{\pi}}\right)}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
Simplified4.8
\[\leadsto \frac{(\left(\frac{1}{b + a} \cdot \left(\frac{1}{b - a} \cdot \color{blue}{\pi}\right)\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
Final simplification4.8
\[\leadsto \frac{(\left(\frac{1}{b + a} \cdot \left(\pi \cdot \frac{1}{b - a}\right)\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{1}{b + a} \cdot \frac{\frac{\pi}{b - a}}{a}\right))_*}{2}\]
