6x(4x^(2)-9y^(2)when divided by 2x(2x-3y) gives

3(2x + 3y)

Step-by-step explanation:

Here, we want to divide

The inner term of the first part can be splitted by the use of the difference of two squares

That is;

given two perfect squares, separated by negative; we can write the factors as;

a^2-b^2 = (a-b)(a + b)

Thus;

4x^2 - 9y^2 = (2x-3y)(2x + 3y)

matching term for term;

6x/2x will give 3

while (2x-3y)(2x + 3y)/(2x-3y) = 2x + 3y

So we have the results of the division as;

3(2x + 3y)