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

Step-by-step Solution

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Final answer to the problem

$x^{2}-x+1+\frac{-1}{1+x}$
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Step-by-step Solution

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  • Solve by factoring
  • Write in simplest form
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
  • Simplify
  • Find the integral
  • Find the derivative
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  • Factor by completing the square
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1

Divide $x^3$ by $1+x$

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

Resulting polynomial

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

Final answer to the problem

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

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Function Plot

Plotting: $x^{2}-x+1+\frac{-1}{1+x}$

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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

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