3x^2-9x-12/x^2+2x+1
=3(x^2-3x-4)/(x+1)^2
=3(x-4)(x+1)/(x+1)^2
=3(x-4)/(x+1)
xy-x-y+1/y^2-2y+1
=xy-y-x+1/(y-1)^2
=y(x-1)-(x-1)/(y-1)^2
=(x-1)(y-1)/(y-1)^2
=(x-1)/(y-1)