\(\frac{3}{7}x-1=\frac{1}{7}x.\left(3x-7\right)\)
\(\Leftrightarrow\frac{3}{7}x-1-\frac{1}{7}x.\left(3x-7\right)=0\)
\(\Leftrightarrow\frac{3}{7}x-1-\left(\frac{3}{7}x^2-x\right)=0\)
\(\Leftrightarrow\frac{3}{7}x-1-\frac{3}{7}x^2+x=0\)
\(\Leftrightarrow\left(\frac{3}{7}x-\frac{3}{7}x^2\right)-\left(1-x\right)=0\)
\(\Leftrightarrow\frac{3}{7}x.\left(1-x\right)-\left(1-x\right)=0\)
\(\Leftrightarrow\left(1-x\right).\left(\frac{3}{7}x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}1-x=0\\\frac{3}{7}x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1-0\\\frac{3}{7}x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\frac{7}{3}\end{matrix}\right.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{1;\frac{7}{3}\right\}.\)
Chúc bạn học tốt!
