document.write( "Question 1132142: Find the sum:\r
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Algebra.Com's Answer #749057 by ikleyn(52778)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "    Find the sum  \"1%2F%28root%283%2C1%29%2Broot%283%2C2%29%2Broot%283%2C4%29%29\" + \"1%2F%28root%283%2C4%29%2Broot%283%2C6%29%2Broot%283%2C9%29%29\" + \"1%2F%28root%283%2C9%29%2Broot%283%2C12%29%2Broot%283%2C16%29%29\"\r\n" );
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document.write( "Use the identity  \"a%5E3-b%5E3\" = \"%28a-b%29%2A%28a%5E2%2Bab+%2B+b%5E2%29\",   which gives you\r\n" );
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document.write( "                  \"1%2F%28a%5E2%2Bab+%2B+b%5E2%29\" = \"%28a-b%29%2F%28a%5E3-b%5E3%29\".   <<<---=== it is how to \"rationalize the fraction\" in this case (!)\r\n" );
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document.write( "In this way,\r\n" );
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document.write( "\"1%2F%28root%283%2C1%29%2Broot%283%2C2%29%2Broot%283%2C4%29%29\" = \"%28root%283%2C2%29-root%283%2C1%29%29%2F%282-1%29\" = \"root%283%2C2%29-1\"              <<<---=== in this case a= 2;  b= 1.\r\n" );
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document.write( "\"1%2F%28root%283%2C4%29%2Broot%283%2C6%29%2Broot%283%2C9%29%29\" = \"%28root%283%2C3%29-root%283%2C2%29%29%2F%283-2%29\" = \"root%283%2C3%29-root%283%2C2%29\";            <<<---=== in this case a= 3;  b= 2.\r\n" );
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document.write( "\"1%2F%28root%283%2C9%29%2Broot%283%2C12%29%2Broot%283%2C16%29%29\" = \"%28root%283%2C4%29-root%283%2C3%29%29%2F%284-3%29\" = \"root%283%2C4%29-root%283%2C3%29\"           <<<---=== in this case a= 4;  b= 3.\r\n" );
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document.write( "So, the long sum of three fractions is equal to\r\n" );
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document.write( "\"root%283%2C2%29-1\" + \"root%283%2C3%29-root%283%2C2%29\" + \"root%283%2C4%29-root%283%2C3%29\" = \"root%283%2C4%29-1\".      ANSWER\r\n" );
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