Step-by-step Solution

Simplify the expression $\frac{x^3+x+5}{x+1}$

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Final Answer

$x^{2}-x+2+\frac{3}{x+1}$

Step-by-step explanation

Problem to solve:

$\frac{x^3+x+5}{x+1}$
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Divide $x^3+x+5$ by $x+1$

$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}-x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}+x\phantom{;}+5\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}-x^{2}+x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{2}+x\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}+5\phantom{;}\phantom{;}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-2x\phantom{;}-2\phantom{;}\phantom{;}}\\\phantom{;;-2x\phantom{;}-2\phantom{;}\phantom{;}-;x^n-;x^n;}\phantom{;}3\phantom{;}\phantom{;}\\\end{array}$
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Resulting polynomial

$x^{2}-x+2+\frac{3}{x+1}$

Final Answer

$x^{2}-x+2+\frac{3}{x+1}$
$\frac{x^3+x+5}{x+1}$

Time to solve it:

~ 0.06 s (SnapXam)