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Solve the rational equation $\frac{5+4x}{3+x}=\frac{1}{3}$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=-\frac{12}{11}$
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Step-by-step Solution

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  • Solve for x
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
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1

Apply fraction cross-multiplication

Learn how to solve rational equations problems step by step online.

$3\left(5+4x\right)=3+x$

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Unlock the first 3 steps of this solution

Learn how to solve rational equations problems step by step online. Solve the rational equation (5+4x)/(3+x)=1/3. Apply fraction cross-multiplication. Solve the product 3\left(5+4x\right). Group the terms of the equation by moving the terms that have the variable x to the left side, and those that do not have it to the right side. Subtract the values 3 and -15.

Final answer to the problem

$x=-\frac{12}{11}$

Exact Numeric Answer

$x=-1.0909091$

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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: $\frac{5+4x}{3+x}-\frac{1}{3}$

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Answer Assistant

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Got a different answer? Verify it!

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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
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

How to improve your answer:

Similar Problems Solved

$\frac{2}{x+1}=\frac{3}{x-1}$

$\frac{4}{x+2}=\frac{6}{x-2}$

$\frac{3}{x+1}-\frac{1}{2}=\frac{1}{3x+3}$

$\frac{2x+4}{5x}=\frac{2}{x}$

$\frac{5}{x-7}=\frac{2}{x-2}$

$\frac{2x+3}{3x}=\frac{x}{2x-3}$

$\frac{x+1}{x-2}=\frac{x-3}{x}$

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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