Algebra.Com's Answer #853899 by ikleyn(53742)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "4/(x-3) + (2x)/(x^2-9) = 1/(x+3)
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document.write( " This problem is very tricky.\r
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document.write( " It contains a hidden trap that's easy to fall into.\r
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document.write( " Tutor @mananth didn't avoid this trap — he fell into it and produced an incorrect solution, \r
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document.write( " for which he deserves a solid F.\r
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document.write( " Below is my correct solution to replace @mananth's incorrect one.\r
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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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document.write( "Solved correctly.\r
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