`x/2-1/x=1/12`
`=>\frac{x^2-2}{2x}=1/12`
`=>12(x^2-2)=2x`
`=>12x^2-24=2x`
`=>12x^2-2x-24=0`
`=>12x^2+16x-18x-24=0`
`=>(3x+4)(4x-6)=0`
`=>2(3x+4)(2x-3)=0`
`=>[(3x+4=0),(2x-3=0):}`
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{4}{3}\\x=\dfrac{3}{2}\end{matrix}\right.\)
ĐKXĐ: \(x\ne0\)
\(\dfrac{x}{2}-\dfrac{1}{x}=\dfrac{1}{12}\)
\(\Leftrightarrow\dfrac{6x^2-12}{12x}=\dfrac{x}{12x}\)
\(\Rightarrow6x^2-12=x\)
\(\Leftrightarrow6x^2+8x-9x-12=0\)
\(\Leftrightarrow2x\left(3x+4\right)-3\left(3x+4\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(3x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\3x+4=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-\dfrac{4}{3}\end{matrix}\right.\)
