Final answer to the problem
$x^{2}-5x+6+\frac{2x-8}{x^2+3x-2}$
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1
Divide $x^4-2x^3-11x^2+30x-20$ by $x^2+3x-2$
$\begin{array}{l}\phantom{\phantom{;}x^{2}+3x\phantom{;}-2;}{\phantom{;}x^{2}-5x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{;}x^{2}+3x\phantom{;}-2\overline{\smash{)}\phantom{;}x^{4}-2x^{3}-11x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-2;}\underline{-x^{4}-3x^{3}+2x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{4}-3x^{3}+2x^{2};}-5x^{3}-9x^{2}+30x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-2-;x^n;}\underline{\phantom{;}5x^{3}+15x^{2}-10x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}5x^{3}+15x^{2}-10x\phantom{;}-;x^n;}\phantom{;}6x^{2}+20x\phantom{;}-20\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}+3x\phantom{;}-2-;x^n-;x^n;}\underline{-6x^{2}-18x\phantom{;}+12\phantom{;}\phantom{;}}\\\phantom{;;-6x^{2}-18x\phantom{;}+12\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}2x\phantom{;}-8\phantom{;}\phantom{;}\\\end{array}$
2
Resulting polynomial
$x^{2}-5x+6+\frac{2x-8}{x^2+3x-2}$
Final answer to the problem
$x^{2}-5x+6+\frac{2x-8}{x^2+3x-2}$
