Question

Tìm x biết : \(\dfrac{2}{\left|x-2\right|+2}=\dfrac{3}{\left|6-3x\right|+1}\)

Answer 1

\(\dfrac{2}{\left|x-2\right|+2}=\dfrac{3}{\left|6-3x\right|+1}\)

\(\dfrac{2}{\left|x-2\right|+2}=\dfrac{3}{3\left|x-2\right|+1}\)

|x-2 | =t ; t>=0

\(\dfrac{2}{t+2}=\dfrac{3}{3t+1}\Leftrightarrow2\left(3t+1\right)=3\left(t+2\right)\)

3t =4 => t =4/3 nhận

|x-2| =4/3 =>\(\left[{}\begin{matrix}x-2=\dfrac{4}{3};x=\dfrac{10}{3}\\x-2=-\dfrac{4}{3};x=\dfrac{2}{3}\end{matrix}\right.\)

Answer 2

2.(/6x-3/+1)=3.(/x-2/+2)

=> 2/6-3x/+2=3./x-2/+6

=> 2.3/2-x/+2=3./2-x/+6

=> 6/2-x/-3/2-x/=6-2=4

=> 3/2-x/=4

=> /2-x/=\(\dfrac{4}{3}\)

=> \(\left[{}\begin{matrix}2-x=\dfrac{4}{3}\\2-x=-\dfrac{4}{3}\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=2-\dfrac{4}{3}=\dfrac{2}{3}\\x=2+\dfrac{4}{3}=\dfrac{10}{3}\end{matrix}\right.\)