## Intermediate Algebra for College Students (7th Edition)

$3y^{2}+\displaystyle \frac{3}{2}y-\frac{7}{4}-\frac{ \frac{7}{4}}{2y-1}$
$\begin{array}{ccccccccccc} & & 3y^{2} & +\displaystyle \frac{3}{2}y& -\displaystyle \frac{7}{4} & \\ & &--&-- &--& \\ 2y-1&) & 6y^{3} &+0 & -5y& +0 & & \\ & & 6y^{3} & -3y^{2} & & & \color{red}{\leftarrow \small{3y^{2}(2y-1) } } \\ & &--&-- & & & \color{red}{ \small{subtract}} \\ & & & 3y^{2} & -5y& +0 & \\ & & & 3y^{2} & -\displaystyle \frac{3}{2}y & & \color{red}{\leftarrow \small{\displaystyle \frac{3}{2}y(2y-1) } }\\ & & &--&-- & &\color{red}{ \small{subtract}} \\ & & & & -\displaystyle \frac{7}{2}y & +0 & \\ & & & & -\displaystyle \frac{7}{2}y & +\displaystyle \frac{7}{4} & \color{red}{\leftarrow \small{-\displaystyle \frac{7}{4}(2y-1) } }\\ & & & &-- & -- &\color{red}{ \small{subtract}} \\ & & & & & -\displaystyle \frac{7}{4} & \end{array}$ Quotient = $3y^{2}+\displaystyle \frac{3}{2}y-\frac{7}{4}$ Remainder = $-\displaystyle \frac{7}{4}$. $\displaystyle \frac{dividend}{divisor}=quotient+\frac{remainder}{divisor}$ $\displaystyle \frac{ 6y^{3}-5y }{2y-1}$ = $3y^{2}+\displaystyle \frac{3}{2}y-\frac{7}{4}-\frac{ \frac{7}{4}}{2y-1}$