Theo đề ta có:
\(\dfrac{a+b}{5}=\dfrac{b+c}{7}=\dfrac{c+d}{8}\)
=> \(\left\{{}\begin{matrix}\dfrac{a+b}{5}=\dfrac{b+c}{7}\Rightarrow7.\left(a+b\right)=5.\left(b+c\right)\\\dfrac{b+c}{7}=\dfrac{c+d}{8}\Rightarrow8.\left(b+c\right)=7.\left(c+d\right)\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}7a+7b=5b+5c\\8b+8c=7c+7d\end{matrix}\right.\)
=> \(\left\{{}\begin{matrix}\dfrac{b}{5b+5}=\dfrac{c}{7a+7}\\\dfrac{c}{7c+7}=\dfrac{d}{8b+8}\end{matrix}\right.\)