\((\left(\frac{-\frac{1}{2}}{b + a}\right) * \left(\frac{\frac{\pi}{b}}{b - a}\right) + \left(\frac{\frac{\pi}{b + a}}{\left(a \cdot 2\right) \cdot \left(b - a\right)}\right))_*\)
- Started with
\[\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
14.7
- Using strategy
rm 14.7
- Applied sub-neg to get
\[\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \color{red}{\left(\frac{1}{a} - \frac{1}{b}\right)} \leadsto \left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \color{blue}{\left(\frac{1}{a} + \left(-\frac{1}{b}\right)\right)}\]
14.7
- Applied distribute-lft-in to get
\[\color{red}{\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(\frac{1}{a} + \left(-\frac{1}{b}\right)\right)} \leadsto \color{blue}{\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \frac{1}{a} + \left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(-\frac{1}{b}\right)}\]
14.7
- Applied simplify to get
\[\color{red}{\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \frac{1}{a}} + \left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(-\frac{1}{b}\right) \leadsto \color{blue}{\frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a}} + \left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(-\frac{1}{b}\right)\]
10.0
- Applied simplify to get
\[\frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a} + \color{red}{\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(-\frac{1}{b}\right)} \leadsto \frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a} + \color{blue}{\left(-\frac{\frac{\frac{\pi}{2}}{b}}{\left(b - a\right) \cdot \left(b + a\right)}\right)}\]
5.1
- Applied taylor to get
\[\frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a} + \left(-\frac{\frac{\frac{\pi}{2}}{b}}{\left(b - a\right) \cdot \left(b + a\right)}\right) \leadsto \frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a} + \left(-\frac{\frac{1}{2} \cdot \frac{\pi}{b}}{\left(b - a\right) \cdot \left(b + a\right)}\right)\]
5.1
- Taylor expanded around 0 to get
\[\frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a} + \left(-\frac{\color{red}{\frac{1}{2} \cdot \frac{\pi}{b}}}{\left(b - a\right) \cdot \left(b + a\right)}\right) \leadsto \frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a} + \left(-\frac{\color{blue}{\frac{1}{2} \cdot \frac{\pi}{b}}}{\left(b - a\right) \cdot \left(b + a\right)}\right)\]
5.1
- Applied simplify to get
\[\frac{\frac{\frac{\pi}{2}}{b + a}}{\left(b - a\right) \cdot a} + \left(-\frac{\frac{1}{2} \cdot \frac{\pi}{b}}{\left(b - a\right) \cdot \left(b + a\right)}\right) \leadsto \frac{\frac{\pi}{b}}{b - a} \cdot \frac{-\frac{1}{2}}{a + b} + \frac{\frac{\frac{\pi}{2}}{a + b}}{\left(b - a\right) \cdot a}\]
0.3
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{\frac{\pi}{b}}{b - a} \cdot \frac{-\frac{1}{2}}{a + b} + \frac{\frac{\frac{\pi}{2}}{a + b}}{\left(b - a\right) \cdot a}} \leadsto \color{blue}{(\left(\frac{-\frac{1}{2}}{b + a}\right) * \left(\frac{\frac{\pi}{b}}{b - a}\right) + \left(\frac{\frac{\pi}{b + a}}{\left(a \cdot 2\right) \cdot \left(b - a\right)}\right))_*}\]
0.3
