Question 1004808
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Solve:
{{{2/(x-1)}}} - {{{1/2}}} = {{{4/(x^2-1)}}}
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<pre>
Your starting equation is

    {{{2/(x-1)}}} - {{{1/2}}} = {{{4/(x^2-1)}}}


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(x^2-1)}}} = 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.    <U>ANSWER</U>
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Solved.