ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Simplify the expression $\frac{x^3+x-1}{x^4+6x^2+9}$

Go!
Symbolic mode
Text mode
Go!
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

##  Final answer to the problem

$\frac{x^3+x-1}{\left(x^{2}+3\right)^{2}}$
Got another answer? Verify it here!

##  Step-by-step Solution 

Specify the solving method

1

The trinomial $x^4+6x^2+9$ is a perfect square trinomial, because it's discriminant is equal to zero

$\Delta=b^2-4ac=6^2-4\left(1\right)\left(9\right) = 0$

Learn how to solve polynomial long division problems step by step online.

$\Delta=b^2-4ac=6^2-4\left(1\right)\left(9\right) = 0$

Learn how to solve polynomial long division problems step by step online. Simplify the expression (x^3+x+-1)/(x^4+6x^2+9). The trinomial x^4+6x^2+9 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial.

##  Final answer to the problem

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

##  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^4+6x^2) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

SnapXam A2

Go!
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.