\(\dfrac{3}{x}+\dfrac{x}{x+1}+\dfrac{x-3}{x}=\dfrac{13}{7}\left(x\ne0;x\ne-1\right)\)
\(< =>\dfrac{3\cdot7\left(x+1\right)}{7x\left(x+1\right)}+\dfrac{7x\cdot x}{7x\left(x+1\right)}+\dfrac{7\left(x-3\right)\left(x+1\right)}{7x\left(x+1\right)}=\dfrac{13x\left(x+1\right)}{7x\left(x+1\right)}\)
suy ra
\(21x+21+7x^2+7\left(x^2+x-3x-3\right)=13x^2+13x\)
\(< =>21x+21+7x^2+7x^2+7x-21x-21=13x^2+13x\)
\(< =>7x^2+7x^2-13x^2+21x+7x-21x-13x+21-21=0\)
\(< =>x^2-6x=0\\ < =>x\left(x-6\right)=0\\ < =>\left[{}\begin{matrix}x=0\\x-6=0\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=0\left(loại\right)\\x=6\left(tm\right)\end{matrix}\right.\)
