document.write( "Question 280750: I need help solving this problem:\r
\n" ); document.write( "\n" ); document.write( "The sum of the reciprocals of two consecutive integers is 5/6 (this should look like a fraction 5 over 6).
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\n" ); document.write( "\n" ); document.write( "Thank you in advance. It says in the directions if there is no solution to write \"no solution\".
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Algebra.Com's Answer #204048 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
I need help solving this problem:\r
\n" ); document.write( "\n" ); document.write( "The sum of the reciprocals of two consecutive integers is 5/6 (this should look like a fraction 5 over 6).
\n" ); document.write( "Find the integers. \r
\n" ); document.write( "\n" ); document.write( "Thank you in advance. It says in the directions if there is no solution to write \"no solution\".
\n" ); document.write( "
\r\n" );
document.write( "Let the consecutive integers be n and n+1:                                                                                                      \r\n" );
document.write( "\"1%2Fn+%2B+1%2F%28n%2B1%29=5%2F6\"\r\n" );
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document.write( "The LCD is \"6n%28n%2B1%29\"\r\n" );
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document.write( "Multiply through by this LCD\r\n" );
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document.write( "\"6%28n%2B1%29+%2B+6n=5n%28n%2B1%29\"\r\n" );
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document.write( "\"6n%2B6%2B6n+=+5n%5E2%2B5n\"\r\n" );
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document.write( "\"12n%2B6=5n%5E2%2B5n\"\r\n" );
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document.write( "\"0=5n%5E2-7n-6\"\r\n" );
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document.write( "\"0=%285n%2B3%29%28n-2%29\"\r\n" );
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document.write( "\"5m%2B3=0\" gives solution \"n=-3%2F5\"\r\n" );
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document.write( "\"n-2=0\" gives solution \"n=2\"\r\n" );
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document.write( "We discard the fractional solution, since it is not an integer.\r\n" );
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document.write( "So the only solution is 2,\r\n" );
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document.write( "so the consecutive integers are 2 and 3:\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "\"1%2F2%2B1%2F3=3%2F6%2B2%2F6=5%2F6\"\r\n" );
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document.write( "It checks.\r\n" );
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document.write( "Edwin

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