Question

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

Answer 1

\(\dfrac{x-1}{3}-\dfrac{x+3}{x}=2\left(đkxđ:x\ne0\right)\)

\(\Leftrightarrow x\left(x-1\right)-3\left(x+3\right)=6x\)

\(\Leftrightarrow x^2-x-3x-9=6x\)

\(\Leftrightarrow x^2-x-3x-6x-9=0\)

\(\Leftrightarrow x^2-10x+25-16=0\)

\(\Leftrightarrow\left(-x-5\right)^2-16=0\)

\(\Leftrightarrow\left(-x-5-4\right)\left(-x-5+4\right)=0\)

\(\Leftrightarrow\left(-x-9\right)\left(-x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}-x-9=0\\-x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-9\\x=-1\end{matrix}\right.\)

Vậy \(S=\left\{-9;-1\right\}\)