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 simplification8.9
\[\leadsto \frac{\frac{\frac{\frac{\pi}{2}}{a + b}}{b - a}}{a} - \frac{\frac{\frac{\frac{\pi}{2}}{a + b}}{b - a}}{b}\]
- Using strategy
rm Applied associate-/l/4.5
\[\leadsto \color{blue}{\frac{\frac{\frac{\pi}{2}}{a + b}}{a \cdot \left(b - a\right)}} - \frac{\frac{\frac{\frac{\pi}{2}}{a + b}}{b - a}}{b}\]
- Using strategy
rm Applied div-inv4.5
\[\leadsto \frac{\frac{\frac{\pi}{2}}{a + b}}{a \cdot \left(b - a\right)} - \frac{\color{blue}{\frac{\frac{\pi}{2}}{a + b} \cdot \frac{1}{b - a}}}{b}\]
Applied associate-/l*0.3
\[\leadsto \frac{\frac{\frac{\pi}{2}}{a + b}}{a \cdot \left(b - a\right)} - \color{blue}{\frac{\frac{\frac{\pi}{2}}{a + b}}{\frac{b}{\frac{1}{b - a}}}}\]
Taylor expanded around 0 3.7
\[\leadsto \frac{\frac{\frac{\pi}{2}}{a + b}}{a \cdot \left(b - a\right)} - \frac{\frac{\frac{\pi}{2}}{a + b}}{\color{blue}{{b}^{2} - a \cdot b}}\]
Simplified0.2
\[\leadsto \frac{\frac{\frac{\pi}{2}}{a + b}}{a \cdot \left(b - a\right)} - \frac{\frac{\frac{\pi}{2}}{a + b}}{\color{blue}{b \cdot \left(b - a\right)}}\]
- Using strategy
rm Applied add-sqr-sqrt0.4
\[\leadsto \frac{\frac{\color{blue}{\sqrt{\frac{\pi}{2}} \cdot \sqrt{\frac{\pi}{2}}}}{a + b}}{a \cdot \left(b - a\right)} - \frac{\frac{\frac{\pi}{2}}{a + b}}{b \cdot \left(b - a\right)}\]
Applied associate-/l*0.5
\[\leadsto \frac{\color{blue}{\frac{\sqrt{\frac{\pi}{2}}}{\frac{a + b}{\sqrt{\frac{\pi}{2}}}}}}{a \cdot \left(b - a\right)} - \frac{\frac{\frac{\pi}{2}}{a + b}}{b \cdot \left(b - a\right)}\]
Final simplification0.5
\[\leadsto \frac{\frac{\sqrt{\frac{\pi}{2}}}{\frac{b + a}{\sqrt{\frac{\pi}{2}}}}}{a \cdot \left(b - a\right)} - \frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot b}\]
