For the expression 4y/3x^2+2xy − 9x/3xy +2y^2

Question

Find the domain.

Answer 1

As written, the domain is all real numbers except x=0, y=0
Assuming the usual carelessness with parentheses, you may have meant

4y/(3x^2+2xy) - 9x/(3xy+2y^2)
= 4y/(x(3x+2y)) - 9x/((y(3x+2y))
= (4y^2 - 9x^2)/(xy(3x+2y))
= (2y-3x)(2y+3x) / xy(2y+3x)
= (2y-3x) / xy
So the domain is 2y+3x≠0 and xy≠0