`ĐKXĐ: x ne +- 1/3`

$\dfrac{12x+1}{6x-2}-\dfrac{9x-5}{3x+1}=\dfrac{108x-36x^2-9}{4\left(9x^2-1\right)}\\
\Leftrightarrow \dfrac{12x+1}{2\left(3x-1\right)}-\dfrac{9x-5}{3x+1}=-\dfrac{36x^2-108x+9}{4\left(3x-1\right)\left(3x+1\right)}\\ \Leftrightarrow \dfrac{12x+1}{2\left(3x-1\right)}-\dfrac{9x-5}{3x+1}+\dfrac{36x^2-108x+9}{4\left(3x-1\right)\left(3x+1\right)}=0\\ \Leftrightarrow \dfrac{2\left(3x+1\right)\left(12x+1\right)}{4\left(3x-1\right)\left(3x+1\right)}-\dfrac{4\left(3x-1\right)\left(9x-5\right)}{4\left(3x-1\right)\left(3x+1\right)}+\dfrac{36x^2-108x+9}{4\left(3x-1\right)\left(3x+1\right)}=0\\ \Leftrightarrow \dfrac{2\left(3x+1\right)\left(12x+1\right)-4\left(3x-1\right)\left(9x-5\right)+36x^2-108x+9}{4\left(3x-1\right)\left(3x+1\right)}=0\\ \Rightarrow 2\left(3x+1\right)\left(12x+1\right)-4\left(3x-1\right)\left(9x-5\right)+36\left(108x+9\right)=0\\
\Leftrightarrow 2\left(36x^2+15x+1\right)-4\left(27x^2-24x+5\right)+36x^2-108x+9=0\\
\Leftrightarrow 72x^2+30x+2-108x^2+96x-20+36x^2-108x+9=0\\\Leftrightarrow 18x-9=0\\ \Leftrightarrow x=\dfrac{1}{2}\left(tm\right)$

Vậy phương trình có tập nghiệm `S={1/2}`