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

Step-by-step Solution

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Solution

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Final answer to the problem

$x=1,\:x=-3$
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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
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1

Move everything to the left hand side of the equation

Learn how to solve operations with infinity problems step by step online.

$\frac{2}{x^2-1}+\frac{-1}{x-1}-\frac{1}{2}=0$

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Unlock the first 3 steps of this solution

Learn how to solve operations with infinity problems step by step online. Solve the rational equation 2/(x^2-1)+-1/(x-1)=1/2. Move everything to the left hand side of the equation. Factor the difference of squares x^2-1 as the product of two conjugated binomials. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete.

Final answer to the problem

$x=1,\:x=-3$

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Function Plot

Plotting: $\frac{2}{x^2-1}+\frac{-1}{x-1}-\frac{1}{2}$

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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

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

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

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

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

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

$\frac{x}{2}=\frac{8}{x}$

Main Topic: Operations with Infinity

Indications for how we should operate with infinity. Very useful to solve limits.

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