In an equation with fractions, we can get rid of the denominators by multiplying each term by the LCD (LCM of denominators).
IN this case the LCM is #color(red)(3(x-1)(x+1))#
#(color(red)(3(cancel(x-1))(x+1))xx2)/cancel(x-1) - (color(red)(cancel3(x-1)(x+1))xx2)/cancel3 =(color(red)(3(x-1)cancel(x+1))xx4)/(cancel(x+1)#
After cancelling the denominators, this leads to a simpler equation.
#6(x+1) -2color(blue)((x-1)(x+1))=12(x-1)" "color(blue)(DOTS)#
#6x+6 -2(x^2-1) = 12x-12#
#6x+6 -2x^2+2=12x-12" make =0"#
#0 = 2x^2+6x-20" "div 2#
#x^2+3x-10= 0" factorise"#
#(x+5)(x-2)= 0#
#x = -5 or x = 2#
