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# Solve the rational equation $\frac{x+1}{x}=\frac{2x+1}{x-1}$

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##  Final answer to the problem

$x=\frac{-1+\sqrt{3}i}{2},\:x=\frac{-1-\sqrt{3}i}{2}$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
Can't find a method? Tell us so we can add it.
1

Apply fraction cross-multiplication

$\left(x+1\right)\left(x-1\right)=x\left(2x+1\right)$

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

$\left(x+1\right)\left(x-1\right)=x\left(2x+1\right)$

Learn how to solve rational equations problems step by step online. Solve the rational equation (x+1)/x=(2x+1)/(x-1). Apply fraction cross-multiplication. Solve the product x\left(2x+1\right). Rearrange the equation. Rewrite the equation.

##  Final answer to the problem

$x=\frac{-1+\sqrt{3}i}{2},\:x=\frac{-1-\sqrt{3}i}{2}$

##  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

SnapXam A2

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5
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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: 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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