Answer
$3x^{2} -xy+2y^{2}$
Work Step by Step
$ \begin{array}{llllllllll}
& & 3x^{2} & -xy & +2y^{2} & & & \color{red}{ \small{Quotient}} & & \\
& & -- & -- & -- & -- & -- & -- & & \\
4x-5y & ) & 12x^{3} & -19x^{2}y & +13xy^{2} & -10y^{3} & & & & \\
& & 12x^{3} & -15x^{2}y & & & & \color{red}{\leftarrow \small{ 3x^{2}(4x-5y) } } & & \\
& & -- & -- & & & & \color{red}{\leftarrow \small{ subtract } } & & \\
& & & -4x^{2}y & +13xy^{2} & -10y^{3} & & & & \\
& & & -4x^{2}y & +5xy^{2} & & & \color{red}{\leftarrow \small{-xy(4x-5y) } } & & \\
& & & -- & -- & & & \color{red}{\leftarrow \small{ subtract }} & & \\
& & & & 8xy^{2} & -10y^{3} & & & & \\
& & & & 8xy^{2} & -10y^{3} & & \color{red}{\leftarrow \small{2y^{2}(4x-5y) } } & & \\
& & & & -- & -- & -- & \color{red}{\leftarrow \small{ subtract }} & & \\
& & & & & 0 & & \color{red}{\leftarrow \small{ Remainder } } & &
\end{array}$
$\displaystyle \frac{12x^{3}-19x^{2}y+13xy^{2}-10y^{3}}{4x-5y}$ = $3x^{2} -xy+2y^{2}$
