Depends what you are expected to know or what method you are told to use.
One learns very early on
Seeing you have the difference of two squares,
So the division to perform using this is obvious.
Maybe you want to use polynomial division?
2x -3
____________________________
2x+3 | 4x^2 0x -9
4x^2 6x
--------------
0 -6x -9
-6x -9
---------
0 0 remainder 0
Directly demonstrating divided by is .