document.write( "Question 1207642: Find the largest positive integer $n$ such that
\n" ); document.write( "\[\frac{(n + 1)^2}{n + 2}\]
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Algebra.Com's Answer #845622 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I wish you wouldn't use notation incompatible with HTML.\r\n" );
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document.write( "Find the largest positive integer n such that\r\n" );
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document.write( "\"%28n%2B1%29%5E2%2F%28n%2B2%29\" is an integer?\r\n" );
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document.write( "I don't think it ever can be a positive integer if n is a positive integer.\r\n" );
document.write( "Let's see why:\r\n" );
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document.write( "\"%28n%5E2%2B2n%2B1%29%2F%28n%2B2%5E%22%22%29\"\r\n" );
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document.write( "Divide it out by long division:\r\n" );
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document.write( "             n + 0\r\n" );
document.write( "n + 2) n2 + 2n + 1\r\n" );
document.write( "       n2 + 2n\r\n" );
document.write( "            0n + 1\r\n" );
document.write( "            0n + 0\r\n" );
document.write( "                 1   \r\n" );
document.write( "       \r\n" );
document.write( "\"%28n%5E2%2B2n%2B1%29%2F%28n%2B2%29\"\"%22%22=%22%22\"\"n%2B1%2F%28n%2B2%29\" and thus will never be a positive \r\n" );
document.write( "integer, because \"1%2F%28n%2B2%29\" will always be a fraction and will\r\n" );
document.write( "never be a positive integer to add to positive integer n to \r\n" );
document.write( "give a positive integer.\r\n" );
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document.write( "Edwin
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