not sure of the question due to lack of () I will guess that you mean
[tex] \frac{4 {x}^{3} {y}^{2} + 2 {x}^{2} {y}^{2} + 3xy }{xy} \\ = \frac{4 {x}^{3} {y}^{2} }{xy} + \frac{2 {x}^{2} {y}^{2} }{xy} + \frac{3xy}{xy} \\ = 4 {x}^{2} {y}^{2} + 2xy + 3[/tex]
I switched x and y with a and b because it is easier to type but same thing :)
