How do I solve $\frac {(x^3-4x^2+5x-6)}{(x^2-x-6)}$ using long division? I tried to solve $\frac {(x^3-4x^2+5x-6)}{(x^2-x-6)}$ using long division...
$x^2-x-6$ / $x^3 -4x^2+5x-6$ \ $x-3 $
$\underline{x^3 - x^2 - 6x}$    -
$-3x^2$
$\underline{-3x^2-3x-18}$ -
$4x+12$

I made some mistake here... How do I solve this step-by-step?

Please see the image below for the long division process - sign changes due to subtraction are highlighted in red. 

