Answer
$ \displaystyle \frac{2x^{4}-x^{3}+9x^{2}}{x^{2}+4} =2x^{2}-x+1+\frac{4x-4}{x^{2}+4}$
Work Step by Step
$\left[\begin{array}{l}
\\
\\
x^{2}+4\ )\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\end{array}\right. \left.\begin{array}{lllll}
2x^{2} & -x & +1 & & \\
\hline 2x^{4} & -x^{3} & +9x^{2} & & \\
2x^{4} & & +8x^{2} & & \\
-- & -- & -- & & \\
& -x^{3} & +x^{2} & & \\
& -x^{3} & & -4x & \\
& -- & -- & -- & \\
& & x^{2} & +4x & \\
& & x^{2} & & +4\\
& & -- & -- & --\\
& & & 4x & -4
\end{array}\right]$
$ \displaystyle \frac{2x^{4}-x^{3}+9x^{2}}{x^{2}+4} =2x^{2}-x+1+\frac{4x-4}{x^{2}+4}$
