Multiply by 1 and you do not change the value. However, 1 comes in many forms.
#color(green)( color(white)("dd")[(3x+1)/(x-2)color(red)(xx1)]color(white)("ddd")-color(white)("dd")[(4x+1)/(x-3)color(red)(xx1)] #
#color(green)([(3x+1)/(x-2)color(red)(xx(x-3)/(x-3))]color(white)("d")-[(4x+1)/(x-3)color(red)(xx(x-2)/(x-2))])#
#color(green)([(3x^2-9x+x-3)/((x-3)(x-2))]-[(4x^2-8x+x-2)/((x-3)(x-2))])#
#color(green)([(3x^2-8x-3)/((x-3)(x-2))]-[(4x^2-7x-2)/((x-3)(x-2))])#
#color(white)("ddddddddd")color(green)( (-x^2-x-1)/((x-3)(x-2) )#
#color(white)("ddddddddd")color(green)( (-(x^2+x+1))/((x-3)(x-2) )#
#color(white)("dddddddd")color(green)( -(x^2+x+1)/((x-3)(x-2) )#