Answer
$2x-3+\displaystyle \frac{2}{4x+9}$
Work Step by Step
$\begin{array}{ccccccccccc}
& &2x & -3 & & \\
& &--&-- &--& \\
4x+9&) & 8x^{2} & +6x& -25 & \\
& & 8x^{2} & +18x& & \color{red}{\leftarrow \small{2x(4x+9) } } \\
& &--&-- & & \color{red}{ \small{subtract}} \\
& & & -12x& -25 & \\
& & & -12x & -27& \color{red}{\leftarrow \small{-3(4x+9) } }\\
& & &--&-- & \color{red}{ \small{subtract}} \\
& & & & +2&\\
\end{array}$
Quotient = $2x-3$
Remainder = $2$.
$\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$
$\displaystyle \frac{ 8x^{2} +6x -25}{4x+9}$ = $2x-3+\displaystyle \frac{2}{4x+9}$
