[tex]\displaystyle\bf\\\frac{8+9x}{36x^{2} -1} +\frac{1}{1-6x} =\frac{2}{6x+1} \\\\\\\frac{8+9x}{(6x -1)(6x+1)} -\frac{1}{6x-1} -\frac{2}{6x+1} =0\\\\\\\frac{8+9x-(6x+1)-2\cdot(6x-1)}{(6x-1)(6x+1)} =0\\\\\\\frac{8+9x-6x-1-12x+2}{(6x-1)(6x+1)} =0\\\\\\\frac{-9x+9}{(6x-1)(6x+1)}=0\\\\\\\left\{\begin{array}{ccc}-9x+9=0\\6x-1\neq 0\\6x+1\neq 0\end{array}\right \\\\\\\left\{\begin{array}{ccc}x=1\\x\neq \dfrac{1}{6} \\x\neq -\dfrac{1}{6} \end{array}\right \\\\\\Otvet \ : \ 1[/tex]