document.write( "Question 1026531: 4/x-3 + 2x\xsquared-9 = 1/x+3 \n" ); document.write( "

Algebra.Com's Answer #853900 by n2(78) $\"\"$ $\"About$

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\n" ); document.write( "4/(x-3) + (2x)/(x^2-9) = 1/(x+3)
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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( "Notice that the domain of this equation is the set of all real numbers except of x = 3 and/or x = -3,\r\n" );
document.write( "where the denominators are not defined.\r\n" );
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document.write( "So, we will work on the domain x =/= -3  and  x =/= 3.\r\n" );
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document.write( "Multiply both sides by  (x^2-3).  You will get \r\n" );
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document.write( "    4(x+3) + 2x = x - 3,\r\n" );
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document.write( "    4x + 12 + 2x = x - 3,\r\n" );
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document.write( "    6x - x = -3 - 12\r\n" );
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document.write( "       5x  =    -15,\r\n" );
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document.write( "        x  =    -15/5 = -3.\r\n" );
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document.write( "But x = -3 is not in the domain.\r\n" );
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document.write( "So, we conclude that the given equation HAS NO solutions in its domain.    <<<---===  ANSWER\r\n" );
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