Final answer to the problem
$\frac{1}{5}x^{2}+\frac{12}{25}x+\frac{99}{125}+\frac{4.584}{5x-2}$
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Step-by-step Solution
Specify the solving method
1
Divide $3+3x+2x^2+x^3$ by $5x-2$
$\begin{array}{l}\phantom{\phantom{;}5x\phantom{;}-2;}{\phantom{;}\frac{1}{5}x^{2}+\frac{12}{25}x\phantom{;}+\frac{99}{125}\phantom{;}\phantom{;}}\\\phantom{;}5x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{3}+2x^{2}+3x\phantom{;}+3\phantom{;}\phantom{;}}\\\phantom{\phantom{;}5x\phantom{;}-2;}\underline{-x^{3}+\frac{2}{5}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}+\frac{2}{5}x^{2};}\phantom{;}\frac{12}{5}x^{2}+3x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}5x\phantom{;}-2-;x^n;}\underline{-\frac{12}{5}x^{2}+\frac{24}{25}x\phantom{;}\phantom{-;x^n}}\\\phantom{;-\frac{12}{5}x^{2}+\frac{24}{25}x\phantom{;}-;x^n;}\phantom{;}\frac{99}{25}x\phantom{;}+3\phantom{;}\phantom{;}\\\phantom{\phantom{;}5x\phantom{;}-2-;x^n-;x^n;}\underline{-\frac{99}{25}x\phantom{;}+1.584\phantom{;}\phantom{;}}\\\phantom{;;-\frac{99}{25}x\phantom{;}+1.584\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}4.584\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$\frac{1}{5}x^{2}+\frac{12}{25}x+\frac{99}{125}+\frac{4.584}{5x-2}$
Final answer to the problem
$\frac{1}{5}x^{2}+\frac{12}{25}x+\frac{99}{125}+\frac{4.584}{5x-2}$