ĐKXĐ: x≠0; x≠-1
Ta có: \(\frac{1}{x+1}-\frac{x-1}{x}=\frac{3x+1}{x\left(x+1\right)}\)
\(\Leftrightarrow\frac{x}{x\left(x+1\right)}-\frac{\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\cdot x}-\frac{3x+1}{x\left(x+1\right)}=0\)
\(\Leftrightarrow x-\left(x^2-1\right)-\left(3x+1\right)=0\)
\(\Leftrightarrow x-x^2+1-3x-1=0\)
\(\Leftrightarrow-x^2-2x=0\)
\(\Leftrightarrow-x\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(ktm\right)\\x+2=0\end{matrix}\right.\Leftrightarrow x=-2\)
Vậy: x=-2