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

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##  Final answer to the problem

$x^{2}-x+2+\frac{3}{x+1}$
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##  Step-by-step Solution 

Specify the solving method

1

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 to the problem

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

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (x^3+x)/(x+1) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.