\(\dfrac{a+b}{a+c}=\dfrac{a-b}{a-c}\)
\(\Rightarrow\left(a+b\right)\left(a-c\right)=\left(a+c\right)\left(a-b\right)\)
\(\Rightarrow a\left(a-c\right)+b\left(a-c\right)=a\left(a-b\right)+c\left(a-b\right)\)
\(\Rightarrow a^2-ac+ab-bc=a^2-ab+ac-bc\)
\(\Rightarrow a^2-ac+ab=a^2-ab+ac\)
\(\Rightarrow a^2+ab+ab=a^2+ac+ac\)
\(\Rightarrow2ab=2ac\)
\(\Rightarrow ab=ac\)
\(\Rightarrow\dfrac{b}{a}=\dfrac{c}{a}\)
Đặt:
\(\dfrac{b}{a}=\dfrac{c}{a}=k\)
\(\Rightarrow\left\{{}\begin{matrix}b=ak\\c=ak\end{matrix}\right.\)
\(\Rightarrow\dfrac{10b^2+9bc+2c^2}{2b^2+bc+2c^2}=\dfrac{10ak^2+9ak^2+2ak^2}{2ak^2+ak^2+2ak^2}\)
\(=\dfrac{21ak^2}{5ak^2}=\dfrac{21}{5}\)
