Question

Cho \(\dfrac{a}{b}=\dfrac{9}{4}\) và \(\dfrac{b}{c}=\dfrac{3}{5}\).Tìm \(\dfrac{a-b}{b-c}\)

Answer 1

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!!!