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Simplify the expression $f\left(x\right)=\frac{x^2}{1+x^5}$

Step-by-step Solution

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Final answer to the problem

$f\left(x\right)=\frac{x^2}{\left(x^{4}-x^{3}+x^{2}-x+1\right)\left(x+1\right)}$
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Step-by-step Solution

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  • Write in simplest form
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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For easier handling, reorder the terms of the polynomial $x^5+1$ from highest to lowest degree

$f\left(x\right)=\frac{x^2}{x^5+1}$

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$f\left(x\right)=\frac{x^2}{x^5+1}$

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Learn how to solve algebraic expressions problems step by step online. Simplify the expression f(x)=(x^2)/(1+x^5). For easier handling, reorder the terms of the polynomial x^5+1 from highest to lowest degree. We can factor the polynomial x^5+1 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 1. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^5+1 will then be.

Final answer to the problem

$f\left(x\right)=\frac{x^2}{\left(x^{4}-x^{3}+x^{2}-x+1\right)\left(x+1\right)}$

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Function Plot

Plotting: $f\left(x\right)+\frac{-x^2}{1+x^5}$

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7
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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

How to improve your answer:

Main Topic: Algebraic expressions

An algebraic expression is a group of terms that are separated by $+$ or $-$ signs.

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