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# Find the roots of $\frac{x^2+x-2}{x^2+5x+6}$

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##  Final answer to the problem

$x=1$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Solve by quadratic formula (general formula)
• Solve for x
• Find the derivative using the definition
• Simplify
• Find the integral
• Find the derivative
• Factor
• Factor by completing the square
• Find the roots
• Find break even points
Can't find a method? Tell us so we can add it.
1

Find the roots of the equation using the Quadratic Formula

$\frac{x^2+x-2}{x^2+5x+6}=0$
2

Factor the trinomial $x^2+5x+6$ finding two numbers that multiply to form $6$ and added form $5$

$\begin{matrix}\left(2\right)\left(3\right)=6\\ \left(2\right)+\left(3\right)=5\end{matrix}$
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Thus

$\frac{x^2+x-2}{\left(x+2\right)\left(x+3\right)}=0$
4

Factor the trinomial $x^2+x-2$ finding two numbers that multiply to form $-2$ and added form $1$

$\begin{matrix}\left(-1\right)\left(2\right)=-2\\ \left(-1\right)+\left(2\right)=1\end{matrix}$
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Thus

$\frac{\left(x-1\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}=0$
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Simplifying

$\frac{x-1}{x+3}=0$
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Multiply both sides of the equation by $x+3$

$x-1=0\left(x+3\right)$
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Any expression multiplied by $0$ is equal to $0$

$x-1=0$
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We need to isolate the dependent variable $x$, we can do that by simultaneously subtracting $-1$ from both sides of the equation

$x-1+1=0+1$
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Canceling terms on both sides

$x=1$

Verify that the solutions obtained are valid in the initial equation

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The valid solutions to the equation are the ones that, when replaced in the original equation, don't make any denominator equal to $0$, since division by zero is not allowed

$x=1$

##  Final answer to the problem

$x=1$

##  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

SnapXam A2

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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

###  Main Topic: Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.