Question 81556
It's a shame it's 18x and not 8x otherwise it would divide nice and easily.  However, if it really is 18x then your answer looks on the right lines to me.
Here's how I did it.
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Starting out, we can divide both the top and the bottom by 2 to get :
(x^2 - 9x + 4)/(x-2)
Now, the top half is almost (x-2)(x-7),  (it looks like you spotted this) since (x-2)(x-7) = 2x^2 - 9x + 14.
So we can re-write as
((x-2)(x-7)-10)/(x-2)
Which leads to:   (x-7) - 10/(x-2)