Ta có:
\(\dfrac{a}{b}=\dfrac{9}{4}\Rightarrow\dfrac{a}{9}=\dfrac{b}{4}\Rightarrow\dfrac{a}{27}=\dfrac{b}{12}\)(1)
\(\dfrac{b}{c}=\dfrac{3}{5}\Rightarrow\dfrac{b}{3}=\dfrac{c}{5}\Rightarrow\dfrac{b}{12}=\dfrac{c}{20}\)(2)
Từ (1) và (2) suy ra:
\(\dfrac{a}{27}=\dfrac{b}{12}=\dfrac{c}{20}\)
Đặt \(\dfrac{a}{27}=\dfrac{b}{12}=\dfrac{c}{20}=k\)
\(\Rightarrow\left\{{}\begin{matrix}a=27k\\b=12k\\c=20k\end{matrix}\right.\)(*)
Thay (*) vào biểu thức \(\dfrac{a-b}{b-c}\) ta có:
\(\dfrac{27k-12k}{12k-20k}=\dfrac{15k}{-8k}=\dfrac{-15}{8}\)
Vậy.............
Chúc bạn học tốt!!!