document.write( "Question 1004808: Solve:
\n" ); document.write( "2/(x-1) - 1/2 = 4/(x^2-1) \n" ); document.write( "

Algebra.Com's Answer #853925 by n2(78) $\"\"$ $\"About$

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\n" ); document.write( " $\"2%2F%28x-1%29\"$ - $\"1%2F2\"$ = $\"4%2F%28x%5E2-1%29\"$
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document.write( "Your starting equation is\r\n" );
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document.write( "     -  = \r\n" );
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document.write( "Its domain is the set of all real numbers except x = -1 and/or x = 1,  where the denominator is zero.\r\n" );
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document.write( "So, we look for solutions in the domain, where x =/= -1, x =/= 1.\r\n" );
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document.write( "Multiply equation by  = 2*(x-1)*(x+1).  You will get\r\n" );
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document.write( "    2*2*(x+1) - 4*2 = x^2 - 1,\r\n" );
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document.write( "    4x + 4 - 8 = x^2 - 1,\r\n" );
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document.write( "    x^2 - 4x + 3 = 0,\r\n" );
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document.write( "    (x-3)*(x-1) = 0.\r\n" );
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document.write( "The roots of this equation are x=3  and  x = 1.\r\n" );
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document.write( "But x=1 is not in the domain of the original equation, so we reject it.\r\n" );
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document.write( "The only solution to the original equation is  x = 3.    ANSWER\r\n" );
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