Simplify the following:

4st/3s(squared) divided by 12tsquared / 9s

[4st/(3s^2)]*[9s/(12t^2)]

= [4t/(3s)][3s/(4t^2)]
= 1/t

To simplify the given expression, we can divide the numerators and the denominators separately.

First, let's divide the numerators:
4st ÷ 3s^2 = 4t ÷ 3

Next, let's divide the denominators:
12t^2 ÷ 9s = 4t^2 ÷ 3s

Now, we can write the simplified expression:
(4t ÷ 3) ÷ (4t^2 ÷ 3s)

To divide by a fraction, we invert the second fraction and multiply:
(4t ÷ 3) * (3s ÷ 4t^2)

When we multiply, we can cancel out common factors:
(4t * 3s) ÷ (3 * 4t^2)

Simplifying further:
12ts ÷ 12t^2

The final simplified expression is:
s ÷ t