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 :)