(4a^3b^2-14a^2b-18ab^2)/(2ab)

To simplify the expression (4a^3b^2 - 14a^2b - 18ab^2) / (2ab), we can simplify each term separately and then divide at the end.

Let's start by simplifying the numerator:
4a^3b^2 can be divided by 2ab to give 2a^2b.
Similarly, -14a^2b can be divided by 2ab to give -7ab.
Lastly, -18ab^2 can also be divided by 2ab to give -9b.

Now we can rewrite the expression as:
(2a^2b - 7ab - 9b) / (2ab).

Since the denominator is the same for each term in the numerator, we can factor it out:
(2a^2b - 7ab - 9b) / (2ab) = (1/2ab)(2a^2b - 7ab - 9b).

Now, let's simplify the numerator further:
To do this, we can factor out the common factor from all the terms.
The greatest common factor (GCF) of 2, a^2, a, b, and -9 is 1.
The GCF of 2a^2, -7a, and -9 is also 1a or a.

Factoring out the GCF a from the numerator, we get:
a(2ab - 7b - 9).

So, the simplified expression is a(2ab - 7b - 9) / (2ab).