Question

\(|\dfrac{3x}{2x-6}|\)-\(|\dfrac{2x-6}{x}|\)=2

Answer 1

ĐKXĐ \(x\ne0,x\ne3\)

Đặt \(|\dfrac{x}{2x-6}|=a\left(a>0\right)\Rightarrow|\dfrac{2x-6}{x}|=\dfrac{1}{a}\)

Phương trình trở thành:

\(3a-\dfrac{1}{a}=2\\ \Rightarrow3a^2-2a-1=0\Leftrightarrow\left(3a+1\right)\left(a-1\right)=0\\ \Leftrightarrow a=1\left(do.a>0\right)\)

\(\Leftrightarrow\left|\dfrac{x}{2x-6}\right|=1\Leftrightarrow x=2x-6...or...x=-\left(2x-6\right)\\ \Leftrightarrow x=6...or...x=2\left(t.m\right)\)