\(a^2+b^2+c^2+2ab-2ac-2bc=a^2+b^2\)
\(\Rightarrow\left(a+b-c\right)^2=a^2+b^2\)
\(\Rightarrow\hept{\begin{cases}a^2=\left(a+b-c\right)^2-b^2=\left(a+b-c-b\right)\left(a+b-c+b\right)=\left(a-c\right)\left(a+2b-c\right)\\b^2=\left(a+b-c\right)^2-a^2=\left(a+b-c-a\right)\left(a+b-c+a\right)=\left(b-c\right)\left(2a+b-c\right)\end{cases}}\)
\(a^2+\left(a-c\right)^2=\left(a-c\right)\left(a+2b-c\right)+\left(a-c\right)^2\)
\(=\left(a-c\right)\left(a+2b-c+a-c\right)=2\left(a-c\right)\left(a+b-c\right)\)
\(b^2+\left(b-c\right)^2=\left(b-c\right)\left(2a+b-c\right)+\left(b-c\right)^2\)
\(=\left(b-c\right)\left(2a+b-c+b-c\right)=2\left(b-c\right)\left(a+b-c\right)\)
Vậy \(\frac{a^2+\left(a-c\right)^2}{b^2+\left(b-c\right)^2}=\frac{2\left(a-c\right)\left(a+b+c\right)}{2\left(b-c\right)\left(a+b+c\right)}=\frac{a-c}{b-c}\)
