Answer
$2x^{3}+6x^{2}+17x+43+\displaystyle \frac{115x-48}{x^{2}-3x+1}$
Work Step by Step
$\left[\begin{array}{l}
\\
x^{2}-3x+1\ )\\
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\\
\\
\\
\\
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\\
\\
\\
\end{array}\right. \left.\begin{array}{llllll}
2x^{3} & +6x^{2} & +17x & +43 & & \\
\hline 2x^{5} & & +x^{3} & -2x^{2} & +3x & -5\\
2x^{5} & -6x^{4} & +2x^{3} & & & \\
-- & -- & -- & & & \\
& 6x^{4} & -x^{3} & -2x^{2} & +3x & -5\\
& 6x^{4} & -18x^{3} & +6x^{2} & & \\
& -- & -- & -- & & \\
& & 17x^{3} & -8x^{2} & +3x & -5\\
& & 17x^{3} & -51x^{2} & +17x & \\
& & -- & -- & -- & \\
& & & 43x^{2} & -14x & -5\\
& & & 43x^{2} & -129x & +43\\
& & & -- & -- & --\\
& & & & 115x & -48\\
& & & & &
\end{array}\right]$
$\displaystyle \frac{2x^{5}+x^{3}-2x^{2}+3x-5}{x^{2}-3x+1}=$
$=2x^{3}+6x^{2}+17x+43+\displaystyle \frac{115x-48}{x^{2}-3x+1}$
