Answer
$\displaystyle \frac{3x^{2}+3x-17}{x+4}=3x^{2}-3x+7+\frac{-29}{x+4}$
Work Step by Step
Using synthetic division,
$\left.\begin{array}{l}
-4\lfloor \\ \\ \\ \end{array}\right.\begin{array}{rrrrr}
3 &9 &-5 &-1& \\\hline
&-12 &12 &-28& \\\hline
3&-3 &7 &-29&\end{array}$
$Q(x)=3x^{2}-3x+7,\quad R(x)=-29$
In the form $ \displaystyle \frac{P(x)}{D(x)}=Q(x)+\frac{R(x)}{D(x)},$
$\displaystyle \frac{3x^{2}+3x-17}{x+4}=3x^{2}-3x+7+\frac{-29}{x+4}$
