SOLUTION: Solve: 2/(x-1) - 1/2 = 4/(x^2-1)

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Question 1004808: Solve:
2/(x-1) - 1/2 = 4/(x^2-1)
Found 3 solutions by mananth, ikleyn, n2:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
2/(x-1) - 1/2 = 4/(x^2-1)
2%2F%28x-1%29+-+1%2F2+=+4%2F%28x%5E2-1%29


2%2F%28x-1%29+-+4%2F%28x%5E2-1%29=1%2F2

Multiply equation by %282%2A%28x%5E2-1%29%29 the LCD
2*2(x+1) -4*2= (x^2-1)
4x+4 -8 = x^2-1
x^2-4x +3=0
x^2-3x-x+3=0
x(x-3)-1(x-3)=0
(x-3)(x-1) =0
x= 3 OR 1



Answer by ikleyn(53746) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve:
2%2F%28x-1%29 - 1%2F2 = 4%2F%28x%5E2-1%29
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


The solution in the post by @mananth is incorrect.

@mananth found two potential solutions, x = 3 OR x=1, and presented them as a final solution.


                It is the  ERROR.


In reality, only ONE of these two potential solutions is a real solution: it is x = 3.

x=1 is not in the domain of the equation, and, therefore, should be rejected.

It is a standard check to reject extraneous solutions, but @mananth neglects to make this check.


The correct answer is x = 3, the only one single unique solution.



Answer by n2(78) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve:
2%2F%28x-1%29 - 1%2F2 = 4%2F%28x%5E2-1%29
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 


Your starting equation is

    2%2F%28x-1%29 - 1%2F2 = 4%2F%28x%5E2-1%29


Its domain is the set of all real numbers except x = -1 and/or x = 1,  where the denominator is zero.

So, we look for solutions in the domain, where x =/= -1, x =/= 1.


Multiply equation by 2%28x%5E2-1%29 = 2*(x-1)*(x+1).  You will get


    2*2*(x+1) - 4*2 = x^2 - 1,

    4x + 4 - 8 = x^2 - 1,

    x^2 - 4x + 3 = 0,

    (x-3)*(x-1) = 0.


The roots of this equation are x=3  and  x = 1.


But x=1 is not in the domain of the original equation, so we reject it.


The only solution to the original equation is  x = 3.    ANSWER

Solved.