document.write( "Question 85653: What is \r
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Algebra.Com's Answer #61858 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"%285-sqrt%283%29%29%2F%283sqrt%285%29%2B4sqrt%283%29%29\"\r\n" );
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document.write( "A. Form the \"conjugate surd\" of the denominator:\r\n" );
document.write( "1. Copy it over.\r\n" );
document.write( "2. Change the sign of the second term only.\r\n" );
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document.write( "So the conjugate surd of denominator \"3sqrt%285%29%2B4sqrt%283%29%29\" is \"3sqrt%285%29-4sqrt%283%29%29\"\r\n" );
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document.write( "B. Put the conjugate surd over itself, forming a fraction which has numerical value 1.\r\n" );
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document.write( "Putting the conjugate over itself:\r\n" );
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document.write( "\"%283sqrt%285%29-4sqrt%283%29%29%2F%283sqrt%285%29-4sqrt%283%29%29\"\r\n" );
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document.write( "C.  Multiply the original fraction by this one. This is permissible \r\n" );
document.write( "because it only amounts to multiplying by 1.\r\n" );
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document.write( "\"%285-sqrt%283%29%29%2F%283sqrt%285%29%2B4sqrt%283%29%29\"×\"%283sqrt%285%29-4sqrt%283%29%29%2F%283sqrt%285%29-4sqrt%283%29%29\"\r\n" );
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document.write( "D. Form into one fraction by indicating the multiplication of the numerators\r\n" );
document.write( "and the denominators:\r\n" );
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document.write( "E. Use FOIL and/or distributive law to multiply out the top and bottom:\r\n" );
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document.write( "Here we use FOIL for both:\r\n" );
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document.write( "             \r\n" );
document.write( "Squaring square roots takes away the radical:\r\n" );
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document.write( "The two middle terms in the bottom cancel out:\r\n" );
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document.write( "\"%2815sqrt%285%29+-+20sqrt%283%29-3sqrt%2815%29%2B4%283%29%29%2F%289%285%29-16%283%29%29\"\r\n" );
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document.write( "\"%2815sqrt%285%29+-+20sqrt%283%29-3sqrt%2815%29%2B12%29%2F%2845-48%29\"\r\n" );
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document.write( "\"%2815sqrt%285%29+-+20sqrt%283%29-3sqrt%2815%29%2B12%29%2F%28-3%29\"\r\n" );
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document.write( "Make into 4 fractions:\r\n" );
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document.write( "Simplify the signs:\r\n" );
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document.write( "\"-15sqrt%285%29%2F3+%2B+20sqrt%283%29%2F3+%2B3sqrt%2815%29%2F3+-12%2F3\"\r\n" );
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document.write( "Cancel what will cancel:\r\n" );
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document.write( "\"-5sqrt%285%29+%2B+20sqrt%283%29%2F3+%2Bsqrt%2815%29+-4\"\r\n" );
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document.write( "You might want to rearrange it so that it begins with a positive term:\r\n" );
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document.write( "\"20sqrt%283%29%2F3-5sqrt%285%29%2Bsqrt%2815%29-4\"\r\n" );
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document.write( "Edwin
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