In order to divide these polynomials, let's use the following property:
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex]So we have:
[tex]\begin{gathered} \frac{14x^4y^3-6x^5y^2}{2x^2y}=\frac{14x^4y^3}{2x^2y}-\frac{6x^5y^2}{2x^2y}=7x^{4-2}y^{3-1}-3x^{5-2}y^{2-1} \\ =7x^2y^2-3x^3y \end{gathered}[/tex]