- Started with
\[\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}\]
25.7
- Using strategy
rm 25.7
- Applied div-sub to get
\[\color{red}{\frac{b \cdot c - a \cdot d}{{c}^2 + {d}^2}} \leadsto \color{blue}{\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a \cdot d}{{c}^2 + {d}^2}}\]
25.8
- Using strategy
rm 25.8
- Applied associate-/l* to get
\[\frac{b \cdot c}{{c}^2 + {d}^2} - \color{red}{\frac{a \cdot d}{{c}^2 + {d}^2}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \color{blue}{\frac{a}{\frac{{c}^2 + {d}^2}{d}}}\]
24.6
- Using strategy
rm 24.6
- Applied *-un-lft-identity to get
\[\frac{b \cdot c}{\color{red}{{c}^2 + {d}^2}} - \frac{a}{\frac{{c}^2 + {d}^2}{d}} \leadsto \frac{b \cdot c}{\color{blue}{1 \cdot \left({c}^2 + {d}^2\right)}} - \frac{a}{\frac{{c}^2 + {d}^2}{d}}\]
24.6
- Applied times-frac to get
\[\color{red}{\frac{b \cdot c}{1 \cdot \left({c}^2 + {d}^2\right)}} - \frac{a}{\frac{{c}^2 + {d}^2}{d}} \leadsto \color{blue}{\frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2}} - \frac{a}{\frac{{c}^2 + {d}^2}{d}}\]
23.2
- Applied taylor to get
\[\frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2} - \frac{a}{\frac{{c}^2 + {d}^2}{d}} \leadsto \frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}}\]
15.5
- Taylor expanded around 0 to get
\[\frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2} - \frac{a}{\color{red}{d + \frac{{c}^2}{d}}} \leadsto \frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2} - \frac{a}{\color{blue}{d + \frac{{c}^2}{d}}}\]
15.5
- Applied simplify to get
\[\frac{b}{1} \cdot \frac{c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}} \leadsto \frac{\frac{b \cdot c}{1}}{c \cdot c + d \cdot d} - \frac{a}{\frac{c}{d} \cdot c + d}\]
15.7
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{\frac{b \cdot c}{1}}{c \cdot c + d \cdot d} - \frac{a}{\frac{c}{d} \cdot c + d}} \leadsto \color{blue}{\frac{c \cdot b}{c \cdot c + {d}^2} - \frac{a}{d + \frac{c \cdot c}{d}}}\]
17.1
