document.write( "Question 1171126: If 3 times the reciprocal of the larger of two consecutive integers is subtracted from 2 times the reciprocal of the smaller, then the result is 1/2. Find the two integers. \n" ); document.write( "

Algebra.Com's Answer #796029 by ikleyn(52874) $\"\"$ $\"About$

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document.write( "The numbers are n and n+1.\r\n" );
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document.write( "The equation is\r\n" );
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document.write( "     -  = .\r\n" );
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document.write( "Multiply both sides by 2n*(n+1).  You will get\r\n" );
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document.write( "    4(n+1) - 6n = n*(n+1)\r\n" );
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document.write( "    4n + 4 - 6n = n^2 + n\r\n" );
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document.write( "    n^2 + 3n - 4 = 0\r\n" );
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document.write( "    (n-1)*(n+4) = 0.\r\n" );
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document.write( "The roots are  n= 1  and  n= -4.\r\n" );
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document.write( "Both roots work.\r\n" );
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document.write( "ANSWER.  There are two solutions.\r\n" );
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document.write( "         First solution represents numbers 1 and 2.\r\n" );
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document.write( "         Second solution represents numbers -4 and -3.\r\n" );
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