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Solve the rational equation $\frac{x^2}{x^3+7x^2+12x}+\frac{-3}{x^2-9}=0$

Step-by-step Solution

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Final Answer

$x=7.582576,\:x=-1.582576$
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Step-by-step Solution

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We can factor the polynomial $x^3+7x^2+12x$ 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 $0$

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Learn how to solve rational equations problems step by step online. Solve the rational equation (x^2)/(x^3+7x^212x)+-3/(x^2-9)=0. We can factor the polynomial x^3+7x^2+12x 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 0. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3+7x^2+12x will then be. We can factor the polynomial x^3+7x^2+12x using synthetic division (Ruffini's rule). We found that -3 is a root of the polynomial.

Final Answer

$x=7.582576,\:x=-1.582576$

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Solve for xFind the rootsSolve by factoringSolve by completing the squareSolve by quadratic formula (general formula)Find break even pointsFind the discriminant

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Plotting: $\frac{x^2}{x^3+7x^2+12x}+\frac{-3}{x^2-9}$

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0
a
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f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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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: Rational Equations

Rational or fractional equations are those equations that contain algebraic fractions, and where the variable or unknown appears in the denominator of at least one of those fractions.

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