\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\)
\(\frac{a^2+c^2}{b^2+d^2}=\frac{c^2\left(\frac{a^2}{c^2}+1\right)}{d^2\left(\frac{b^2}{d^2}+1\right)}\)
Do đó:\(\frac{a}{c}=\frac{b}{d}\rightarrow\frac{a^2}{c^2}=\frac{b^2}{d^2}\rightarrow\frac{a^2}{c^2}+1=\frac{b^2}{d^2}+1\)
\(\Rightarrow\frac{a^2+c^2}{b^2+d^2}=\frac{c^2}{d^2}=\frac{c}{d}.\frac{c}{d}=\frac{c}{d}.\frac{a}{b}=\frac{ac}{bd}\)
Nhớ tick cho mình nha!