Whats the common denominator of this

(2/x-3) and (3/2x+3)

the two denominators are (x-3) and (2x+3)
multiply them together:
2(x^2)-3x-9 is your common denominator.

the first fraction must be multiplied by (2x+3) over (2x+3)
*this is like multiplying it by 1, it doesn't change the fraction
(4x+6)/[2(x^2)-3x-9] is the first fraction

the second fraction must be multiplied by (x-3) over (x-3)
*this is like multiplying it by 1, it doesn't change the fraction
(3x-9)/[2(x^2)-3x-9] is the second fraction

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