\(\frac{b \cdot c}{(d * d + \left({c}^2\right))_*} - \frac{a}{(\left(\frac{c}{d}\right) * c + d)_*}\)
- 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
- Applied taylor to get
\[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\frac{{c}^2 + {d}^2}{d}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}}\]
17.1
- Taylor expanded around 0 to get
\[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{red}{d + \frac{{c}^2}{d}}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{\color{blue}{d + \frac{{c}^2}{d}}}\]
17.1
- Applied taylor to get
\[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}}\]
17.1
- Taylor expanded around 0 to get
\[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \color{red}{\frac{{c}^2}{d}}} \leadsto \frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \color{blue}{\frac{{c}^2}{d}}}\]
17.1
- Applied simplify to get
\[\frac{b \cdot c}{{c}^2 + {d}^2} - \frac{a}{d + \frac{{c}^2}{d}} \leadsto \frac{c \cdot b}{(d * d + \left(c \cdot c\right))_*} - \frac{a}{d + \frac{c}{\frac{d}{c}}}\]
15.7
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{c \cdot b}{(d * d + \left(c \cdot c\right))_*} - \frac{a}{d + \frac{c}{\frac{d}{c}}}} \leadsto \color{blue}{\frac{b \cdot c}{(d * d + \left({c}^2\right))_*} - \frac{a}{(\left(\frac{c}{d}\right) * c + d)_*}}\]
15.7
