1) $(x-1)(x+1)-(x-2)^2=4$
$\to x^2 -1 -x^2 -4x-4=4$
$\to -4x -5 -4 =0$
$\to -4x -9 = 0$
$\to x = -\dfrac{9}{4}$
2) $\dfrac{x}{3} -\dfrac{2x+1}{2}=\dfrac{5x}{6}$
$\to \dfrac{x}{3}-\dfrac{2x+1}{2}-\dfrac{5x}{6}=0$
$\to \dfrac{2x-3.(2x+1)-5x}{6}=0$
$\to \dfrac{ 2x -6x-3-5x}{6}=0$
$\to \dfrac{-3-9x}{6}=0$
$\to \dfrac{-3(1+3x)}{6}=0$
$\to\dfrac{-1-3x}{2}=0$
$\to -1-3x=0$
$\to x= -\dfrac{1}{3}$
3)$\dfrac{3x-2}{6}-\dfrac{4-3x}{18}=\dfrac{4-x}{9}$
$\to \dfrac{3x-2}{6}-\dfrac{4-3x}{18}-\dfrac{4-x}{9}=0$
$\to \dfrac{3(3x-2)-(4-3x)-2(4-x)}{18}=0$
$\to \dfrac{9x-6-4+3x-8+2x}{18}=0$
$\to \dfrac{14x-18}{18}=0$
$\to \dfrac{2(7x-9)}{18}=0$
$\to \dfrac{7x-9}{9}=0$
$\to 7x-9=0 \to x=\dfrac{9}{7}$
