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Solve the rational equation $\frac{2x+6}{3x}=x-8$

Step-by-step Solution

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Solution

Final answer to the problem

$x=\frac{13+\sqrt{187}}{3},\:x=\frac{13-\sqrt{187}}{3}$
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Step-by-step Solution

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  • Solve for x
  • Find the derivative using the definition
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1

Factor the polynomial $2x+6$ by it's greatest common factor (GCF): $2$

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$\frac{2\left(x+3\right)}{3x}=x-8$

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Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. Solve the rational equation (2x+6)/(3x)=x-8. Factor the polynomial 2x+6 by it's greatest common factor (GCF): 2. Multiply both sides of the equation by 3x. Solve the product 2\left(x+3\right). Solve the product 3\left(x-8\right)x.

Final answer to the problem

$x=\frac{13+\sqrt{187}}{3},\:x=\frac{13-\sqrt{187}}{3}$

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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

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Function Plot

Plotting: $\frac{2x+6}{3x}-x+8$

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1
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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
D□x
∫
∫◻
|◻|
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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