(x^2 - x-6) 8
--------------- = ----------
x^2 -4x+3 6
factor on the left and simplify on the right
(x-3) (x+2) 4
-------------- = ----
(x-3)(x-1) 3
cancel factors on the left
(x+2) 4
-------------- = ----
(x-1) 3
use cross products
3(x+2) = 4(x-1)
3x+6 = 4x-4
subtract 3x from each side
6 = x-4
add 4 to each side
10 =x