\(\frac{(c * a + \left(b \cdot d\right))_*}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}\)
- Started with
\[\frac{a \cdot c + b \cdot d}{{c}^2 + {d}^2}\]
12.6
- Using strategy
rm 12.6
- Applied add-sqr-sqrt to get
\[\frac{a \cdot c + b \cdot d}{\color{red}{{c}^2 + {d}^2}} \leadsto \frac{a \cdot c + b \cdot d}{\color{blue}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}}\]
12.5
- Applied add-sqr-sqrt to get
\[\frac{\color{red}{a \cdot c + b \cdot d}}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2} \leadsto \frac{\color{blue}{{\left(\sqrt{a \cdot c + b \cdot d}\right)}^2}}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}\]
22.1
- Applied square-undiv to get
\[\color{red}{\frac{{\left(\sqrt{a \cdot c + b \cdot d}\right)}^2}{{\left(\sqrt{{c}^2 + {d}^2}\right)}^2}} \leadsto \color{blue}{{\left(\frac{\sqrt{a \cdot c + b \cdot d}}{\sqrt{{c}^2 + {d}^2}}\right)}^2}\]
22.1
- Applied simplify to get
\[{\color{red}{\left(\frac{\sqrt{a \cdot c + b \cdot d}}{\sqrt{{c}^2 + {d}^2}}\right)}}^2 \leadsto {\color{blue}{\left(\frac{\sqrt{(c * a + \left(d \cdot b\right))_*}}{\sqrt{c^2 + d^2}^*}\right)}}^2\]
19.9
- Applied taylor to get
\[{\left(\frac{\sqrt{(c * a + \left(d \cdot b\right))_*}}{\sqrt{c^2 + d^2}^*}\right)}^2 \leadsto {\left(\frac{\sqrt{(c * a + \left(b \cdot d\right))_*}}{\sqrt{c^2 + d^2}^*}\right)}^2\]
19.9
- Taylor expanded around 0 to get
\[{\left(\frac{\color{red}{\sqrt{(c * a + \left(b \cdot d\right))_*}}}{\sqrt{c^2 + d^2}^*}\right)}^2 \leadsto {\left(\frac{\color{blue}{\sqrt{(c * a + \left(b \cdot d\right))_*}}}{\sqrt{c^2 + d^2}^*}\right)}^2\]
19.9
- Applied simplify to get
\[{\left(\frac{\sqrt{(c * a + \left(b \cdot d\right))_*}}{\sqrt{c^2 + d^2}^*}\right)}^2 \leadsto \frac{(c * a + \left(b \cdot d\right))_*}{\sqrt{c^2 + d^2}^* \cdot \sqrt{c^2 + d^2}^*}\]
8.0
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{(c * a + \left(b \cdot d\right))_*}{\sqrt{c^2 + d^2}^* \cdot \sqrt{c^2 + d^2}^*}} \leadsto \color{blue}{\frac{(c * a + \left(b \cdot d\right))_*}{{\left(\sqrt{c^2 + d^2}^*\right)}^2}}\]
8.0
