Question

Tính giá trị biểu thức :

A= \(\dfrac{3a-2b}{a-3b}\) với \(\dfrac{a}{b}=\dfrac{10}{3}\)

Answer 1

Đặt \(a=\dfrac{10}{3}b\Rightarrow\dfrac{3.\dfrac{10}{3}b-2b}{\dfrac{10}{3}b-3b}=\dfrac{10b-2b}{\dfrac{1}{3}b}=\dfrac{8}{\dfrac{1}{3}}=24\)

Answer 2

Giải:

\(\dfrac{a}{b}=\dfrac{10}{3}\Rightarrow\dfrac{a}{10}=\dfrac{b}{3}.\)

Đặt \(\dfrac{a}{10}=\dfrac{b}{3}=k\Rightarrow a=10k;b=3k.\)

Ta có:

\(A=\dfrac{3a-2b}{a-3b}=\dfrac{3.10k-2.3k}{10k-3.3k}=\dfrac{30k-6k}{10k-9k}=\dfrac{\left(30-6\right)k}{\left(10-9\right)k}=\dfrac{24}{1}=24.\)

Vậy \(A=24.\)