Initial program 14.7
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
- Using strategy
rm Applied frac-sub14.7
\[\leadsto \left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \color{blue}{\frac{1 \cdot b - a \cdot 1}{a \cdot b}}\]
Applied associate-*l/14.7
\[\leadsto \color{blue}{\frac{\pi \cdot \frac{1}{b \cdot b - a \cdot a}}{2}} \cdot \frac{1 \cdot b - a \cdot 1}{a \cdot b}\]
Applied frac-times14.7
\[\leadsto \color{blue}{\frac{\left(\pi \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(1 \cdot b - a \cdot 1\right)}{2 \cdot \left(a \cdot b\right)}}\]
Simplified0.2
\[\leadsto \frac{\color{blue}{\frac{\pi}{b + a}}}{2 \cdot \left(a \cdot b\right)}\]
- Using strategy
rm Applied clear-num0.3
\[\leadsto \frac{\color{blue}{\frac{1}{\frac{b + a}{\pi}}}}{2 \cdot \left(a \cdot b\right)}\]
- Using strategy
rm Applied div-inv0.3
\[\leadsto \frac{\frac{1}{\color{blue}{\left(b + a\right) \cdot \frac{1}{\pi}}}}{2 \cdot \left(a \cdot b\right)}\]
Applied add-sqr-sqrt0.3
\[\leadsto \frac{\frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{\left(b + a\right) \cdot \frac{1}{\pi}}}{2 \cdot \left(a \cdot b\right)}\]
Applied times-frac0.3
\[\leadsto \frac{\color{blue}{\frac{\sqrt{1}}{b + a} \cdot \frac{\sqrt{1}}{\frac{1}{\pi}}}}{2 \cdot \left(a \cdot b\right)}\]
Applied times-frac0.3
\[\leadsto \color{blue}{\frac{\frac{\sqrt{1}}{b + a}}{2} \cdot \frac{\frac{\sqrt{1}}{\frac{1}{\pi}}}{a \cdot b}}\]
Simplified0.3
\[\leadsto \color{blue}{\frac{\frac{1}{2}}{a + b}} \cdot \frac{\frac{\sqrt{1}}{\frac{1}{\pi}}}{a \cdot b}\]
Simplified0.3
\[\leadsto \frac{\frac{1}{2}}{a + b} \cdot \color{blue}{\frac{\frac{\pi}{a}}{b}}\]
- Using strategy
rm Applied associate-*l/0.3
\[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot \frac{\frac{\pi}{a}}{b}}{a + b}}\]
Final simplification0.3
\[\leadsto \frac{\frac{\frac{\pi}{a}}{b} \cdot \frac{1}{2}}{a + b}\]
