Initial program 14.9
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
Initial simplification9.8
\[\leadsto \frac{(\left(\frac{\pi}{2}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{2}}{a}\right))_*}{\left(a + b\right) \cdot \left(b - a\right)}\]
- Using strategy
rm Applied *-un-lft-identity9.8
\[\leadsto \frac{\color{blue}{1 \cdot (\left(\frac{\pi}{2}\right) \cdot \left(\frac{-1}{b}\right) + \left(\frac{\frac{\pi}{2}}{a}\right))_*}}{\left(a + b\right) \cdot \left(b - a\right)}\]
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
\[\leadsto \frac{1}{a + b} \cdot \color{blue}{\frac{\frac{\pi}{a \cdot 2} - \frac{\pi}{2 \cdot b}}{b - a}}\]
Taylor expanded around -inf 0.3
\[\leadsto \frac{1}{a + b} \cdot \color{blue}{\left(\frac{1}{2} \cdot \frac{\pi}{a \cdot b}\right)}\]
- Using strategy
rm Applied pow10.3
\[\leadsto \frac{1}{a + b} \cdot \color{blue}{{\left(\frac{1}{2} \cdot \frac{\pi}{a \cdot b}\right)}^{1}}\]
Applied pow10.3
\[\leadsto \color{blue}{{\left(\frac{1}{a + b}\right)}^{1}} \cdot {\left(\frac{1}{2} \cdot \frac{\pi}{a \cdot b}\right)}^{1}\]
Applied pow-prod-down0.3
\[\leadsto \color{blue}{{\left(\frac{1}{a + b} \cdot \left(\frac{1}{2} \cdot \frac{\pi}{a \cdot b}\right)\right)}^{1}}\]
Simplified0.2
\[\leadsto {\color{blue}{\left(\frac{\frac{\pi}{a + b}}{\frac{b \cdot a}{\frac{1}{2}}}\right)}}^{1}\]
Final simplification0.2
\[\leadsto \frac{\frac{\pi}{a + b}}{\frac{b \cdot a}{\frac{1}{2}}}\]
