Given #(x+1)/(x-3) = 4 - 12/(x^2-2x-3)#
and
assuming that #x^2-2x-3 != 0# (otherwise we have an undefined division)
Note that #x^2-2x-3= (x-3)((x+1)#
So we can re-write the equation with a common denominators as
#color(white)("XXXXX")##((x+1)(x+1))/(x^2-2x-3) = (4(x^2-2x-3) - 12)/(x^2-2x-3)#
and since #x^2-2x-3 != 0#
#color(white)("XXXXX")##((x+1)(x+1)) = (4(x^2-2x-3) - 12)#
Simplifying
#color(white)("XXXXX")##x^2+2x+1 = 4x^2-8x -24#
#color(white)("XXXXX")##3x^2-10x-25 = 0#
#color(white)("XXXXX")##(3x+5)(x-5) = 0#
#x= -5/3# or #x=5#
