Answer
$(\displaystyle \frac{f}{g})(x)= 2x^{2} -9x+10$
Work Step by Step
$(\displaystyle \frac{f}{g})(x)=\frac{8x^{3}-38x^{2}+49x-10}{4x-1}$
$=(8x^{3}-38x^{2}+49x-10)\div(4x-1)$
$ \begin{array}{llllllllll}
& & 2x^{2} & -9x & +10 & & & \color{red}{ \small{quotient}} & & \\
& & -- & -- & -- & -- & -- & -- & & \\
4x-1 & ) & 8x^{3} & -38x^{2} & +49x & -10 & & & & \\
& & 8x^{3} & -2x^{2} & & & & \color{red}{\leftarrow \small{ 2x^{2}(4x-1) } } & & \\
& & -- & -- & & & & \color{red}{\leftarrow \small{ subtract } } & & \\
& & & -36x^{2} & +49x & -10 & & & & \\
& & & -36x^{2} & +9x & & & \color{red}{\leftarrow \small{-9x(4x-1) } } & & \\
& & & -- & -- & & & \color{red}{\leftarrow \small{ subtract }} & & \\
& & & & 40x & -10 & & & & \\
& & & & 40x & -10 & & \color{red}{\leftarrow \small{ 10(4x-1) } } & & \\
& & & & -- & -- & & \color{red}{\leftarrow \small{ subtract } } & & \\
& & & & & & & & & \\
& & & & & 0 & & \color{red}{\leftarrow \small{ Remainder } } & &
\end{array} $
$(\displaystyle \frac{f}{g})(x)= 2x^{2} -9x+10$
