Answer
$4x^{2} +5xy-y^{2}$
Work Step by Step
$ \begin{array}{llllllllll}
& & 4x^{2} & +5xy & -y^{2} & & & \color{red}{ \small{Quotient}} & & \\
& & -- & -- & -- & -- & -- & -- & & \\
x-3y & ) & 4x^{3} & -7x^{2}y & -16xy^{2} & +3y^{3} & & & & \\
& & 4x^{2} & -12x^{2}y & & & & \color{red}{\leftarrow \small{ 4x^{2}(x-3y) } } & & \\
& & -- & -- & & & & \color{red}{\leftarrow \small{ subtract } } & & \\
& & & 5x^{2}y & -16xy^{2} & +3y^{3} & & & & \\
& & & 5x^{2}y & -15xy^{2} & & & \color{red}{\leftarrow \small{5xy(x^{2}+x+1) } } & & \\
& & & -- & -- & & & \color{red}{\leftarrow \small{ subtract }} & & \\
& & & & -xy^{2} & +3y^{3} & & & & \\
& & & & -xy^{2} & +3y^{3} & & \color{red}{\leftarrow \small{y^{2}(x^{2}+x+1) } } & & \\
& & & & -- & -- & & \color{red}{\leftarrow \small{ subtract }} & & \\
& & & & & 0 & & \color{red}{\leftarrow \small{ Remainder } } & &
\end{array}$
$\displaystyle \frac{4x^{3}-7x^{2}y-16xy^{2}+3y^{3}}{x-3y}$ = $4x^{2} +5xy-y^{2}$
