\((\left(c \cdot t - i \cdot y\right) * j + \left(x \cdot \left(y \cdot z - a \cdot t\right)\right))_* - b \cdot \left(z \cdot c - i \cdot a\right)\)
- Started with
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
11.5
- Applied simplify to get
\[\color{red}{\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(\left(y \cdot z - t \cdot a\right) \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)}\]
11.5
- Using strategy
rm 11.5
- Applied flip-- to get
\[(\left(c \cdot t - i \cdot y\right) * j + \left(\color{red}{\left(y \cdot z - t \cdot a\right)} \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(\color{blue}{\frac{{\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2}{y \cdot z + t \cdot a}} \cdot x\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
23.6
- Applied associate-*l/ to get
\[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{\left(\frac{{\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2}{y \cdot z + t \cdot a} \cdot x\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{\left(\frac{\left({\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2\right) \cdot x}{y \cdot z + t \cdot a}\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
25.9
- Applied taylor to get
\[(\left(c \cdot t - i \cdot y\right) * j + \left(\frac{\left({\left(y \cdot z\right)}^2 - {\left(t \cdot a\right)}^2\right) \cdot x}{y \cdot z + t \cdot a}\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
11.8
- Taylor expanded around inf to get
\[(\left(c \cdot t - i \cdot y\right) * j + \color{red}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(c \cdot t - i \cdot y\right) * j + \color{blue}{\left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right)})_* - b \cdot \left(c \cdot z - i \cdot a\right)\]
11.8
- Applied simplify to get
\[(\left(c \cdot t - i \cdot y\right) * j + \left(y \cdot \left(x \cdot z\right) - a \cdot \left(t \cdot x\right)\right))_* - b \cdot \left(c \cdot z - i \cdot a\right) \leadsto (\left(t \cdot c - y \cdot i\right) * j + \left(\left(y \cdot z\right) \cdot x - \left(x \cdot t\right) \cdot a\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)\]
11.7
- Applied final simplification
- Applied simplify to get
\[\color{red}{(\left(t \cdot c - y \cdot i\right) * j + \left(\left(y \cdot z\right) \cdot x - \left(x \cdot t\right) \cdot a\right))_* - b \cdot \left(z \cdot c - a \cdot i\right)} \leadsto \color{blue}{(\left(c \cdot t - i \cdot y\right) * j + \left(x \cdot \left(y \cdot z - a \cdot t\right)\right))_* - b \cdot \left(z \cdot c - i \cdot a\right)}\]
11.5
