2x+5 x+4
------ - ---------
x^2+3x+2 x^2+3x+2
i keep getting
x+9
------------
(x+1)(x+2)
no. just look at numerator.
(2x+5)/k - (x+4)/k= (2x-x +5-4)/k
you are ok on factoring the denominator, but I think if you do the numberator correctly, the x+1 will divide out.