Final answer to the problem
$x^{2}-3x-2+\frac{8}{x+1}$
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Step-by-step Solution
1
Divide $x^3-2x^2-5x+6$ by $x+1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}-3x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}-2x^{2}-5x\phantom{;}+6\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}-3x^{2}-5x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}3x^{2}+3x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}3x^{2}+3x\phantom{;}-;x^n;}-2x\phantom{;}+6\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{\phantom{;}2x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;;\phantom{;}2x\phantom{;}+2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}8\phantom{;}\phantom{;}\\\end{array}$
$x^{2}-3x-2+\frac{8}{x+1}$
Final answer to the problem
$x^{2}-3x-2+\frac{8}{x+1}$