\(\frac{2x-1}{x}+\frac{3-x}{4}=2\)
\(ĐKXĐ:x\ne0\)
\(MTC:4x\)
\(\frac{4\left(2x-1\right)}{4x}+\frac{x\left(3-x\right)}{4x}=\frac{8x}{4x}\)
\(\Rightarrow4\left(2x-1\right)+x\left(x-3\right)=8x\)
\(\Leftrightarrow8x-4+x^2-3x=8x\)
\(\Leftrightarrow8x-4+x^2-3x-8x=0\)
\(\Leftrightarrow x^2-3x-4=0\)
\(\Leftrightarrow x^2-4x+x-4=0\)
\(\Leftrightarrow\left(x^2-4x\right)+\left(x-4\right)=0\)
\(\Leftrightarrow x\left(x-4\right)+\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x+1\right)=0\)
Hoặc\(\hept{\begin{cases}x-4=0\\x+1=0\end{cases}\Leftrightarrow\hept{\begin{cases}x=4\left(N\right)\\x=-1\left(N\right)\end{cases}}}\)
Vậy tập nghiệp của pt là \(S=\left\{-1;4\right\}\)
