Initial program 14.3
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
Initial simplification0.3
\[\leadsto \frac{\left(\frac{1}{a} - \frac{1}{b}\right) \cdot \frac{\frac{\pi}{2}}{b - a}}{a + b}\]
- Using strategy
rm Applied pow10.3
\[\leadsto \frac{\left(\frac{1}{a} - \frac{1}{b}\right) \cdot \color{blue}{{\left(\frac{\frac{\pi}{2}}{b - a}\right)}^{1}}}{a + b}\]
Applied pow10.3
\[\leadsto \frac{\color{blue}{{\left(\frac{1}{a} - \frac{1}{b}\right)}^{1}} \cdot {\left(\frac{\frac{\pi}{2}}{b - a}\right)}^{1}}{a + b}\]
Applied pow-prod-down0.3
\[\leadsto \frac{\color{blue}{{\left(\left(\frac{1}{a} - \frac{1}{b}\right) \cdot \frac{\frac{\pi}{2}}{b - a}\right)}^{1}}}{a + b}\]
Simplified0.3
\[\leadsto \frac{{\color{blue}{\left(\frac{\frac{\pi}{a} - \frac{\pi}{b}}{\left(b - a\right) \cdot 2}\right)}}^{1}}{a + b}\]
- Using strategy
rm Applied *-un-lft-identity0.3
\[\leadsto \frac{{\left(\frac{\color{blue}{1 \cdot \left(\frac{\pi}{a} - \frac{\pi}{b}\right)}}{\left(b - a\right) \cdot 2}\right)}^{1}}{a + b}\]
Applied times-frac0.3
\[\leadsto \frac{{\color{blue}{\left(\frac{1}{b - a} \cdot \frac{\frac{\pi}{a} - \frac{\pi}{b}}{2}\right)}}^{1}}{a + b}\]
Applied unpow-prod-down0.3
\[\leadsto \frac{\color{blue}{{\left(\frac{1}{b - a}\right)}^{1} \cdot {\left(\frac{\frac{\pi}{a} - \frac{\pi}{b}}{2}\right)}^{1}}}{a + b}\]
Applied associate-/l*0.3
\[\leadsto \color{blue}{\frac{{\left(\frac{1}{b - a}\right)}^{1}}{\frac{a + b}{{\left(\frac{\frac{\pi}{a} - \frac{\pi}{b}}{2}\right)}^{1}}}}\]
Simplified0.3
\[\leadsto \frac{\color{blue}{\frac{1}{b - a}}}{\frac{a + b}{{\left(\frac{\frac{\pi}{a} - \frac{\pi}{b}}{2}\right)}^{1}}}\]
Final simplification0.3
\[\leadsto \frac{\frac{1}{b - a}}{\frac{b + a}{\frac{\frac{\pi}{a} - \frac{\pi}{b}}{2}}}\]
