[tex]\displaystyle\bf\\\frac{1}{x-1} =\frac{2}{x+1} \\\\\\\frac{1}{x-1} -\frac{2}{x+1} =0\\\\\\\frac{x+1-2x+2}{(x-1)(x+1)} =0\\\\\\\frac{-x+3}{(x-1)(x+1)} =0\\\\\\\left\{\begin{array}{ccc}-x+3=0\\x-1\neq 0\\x+1\neq 0\end{array}\right\\\\\\\left\{\begin{array}{ccc}x=3\\x\neq 1\\x\neq -1\end{array}\right\\\\\\Otvet \ : \ 3[/tex]