Initial program 14.5
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
Simplified14.5
\[\leadsto \color{blue}{\frac{\frac{\pi}{b \cdot b - a \cdot a}}{\frac{2}{\frac{1}{a} - \frac{1}{b}}}}\]
- Using strategy
rm Applied difference-of-squares9.7
\[\leadsto \frac{\frac{\pi}{\color{blue}{\left(b + a\right) \cdot \left(b - a\right)}}}{\frac{2}{\frac{1}{a} - \frac{1}{b}}}\]
Applied associate-/r*9.1
\[\leadsto \frac{\color{blue}{\frac{\frac{\pi}{b + a}}{b - a}}}{\frac{2}{\frac{1}{a} - \frac{1}{b}}}\]
- Using strategy
rm Applied frac-sub9.2
\[\leadsto \frac{\frac{\frac{\pi}{b + a}}{b - a}}{\frac{2}{\color{blue}{\frac{1 \cdot b - a \cdot 1}{a \cdot b}}}}\]
Applied associate-/r/9.1
\[\leadsto \frac{\frac{\frac{\pi}{b + a}}{b - a}}{\color{blue}{\frac{2}{1 \cdot b - a \cdot 1} \cdot \left(a \cdot b\right)}}\]
Applied div-inv9.1
\[\leadsto \frac{\color{blue}{\frac{\pi}{b + a} \cdot \frac{1}{b - a}}}{\frac{2}{1 \cdot b - a \cdot 1} \cdot \left(a \cdot b\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{\frac{\pi}{b + a}}{\frac{2}{1 \cdot b - a \cdot 1}} \cdot \frac{\frac{1}{b - a}}{a \cdot b}}\]
Simplified0.3
\[\leadsto \color{blue}{\left(\frac{\pi}{\left(b + a\right) \cdot 2} \cdot \left(b - a\right)\right)} \cdot \frac{\frac{1}{b - a}}{a \cdot b}\]
- Using strategy
rm Applied clear-num0.4
\[\leadsto \left(\color{blue}{\frac{1}{\frac{\left(b + a\right) \cdot 2}{\pi}}} \cdot \left(b - a\right)\right) \cdot \frac{\frac{1}{b - a}}{a \cdot b}\]
Final simplification0.4
\[\leadsto \left(\left(b - a\right) \cdot \frac{1}{\frac{\left(b + a\right) \cdot 2}{\pi}}\right) \cdot \frac{\frac{1}{b - a}}{a \cdot b}\]
