document.write( "Question 878194: One positive integer is 5 more than the other. When the reciprocal of the larger number is subtracted from the reciprocal of the smaller, the result is 5/14. Find the two integers. My answers are 2 and -7 but I am being told you cannot have a negative number. If so, why? \n" ); document.write( "
Algebra.Com's Answer #529754 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "I think you thought the two values for the smaller \r\n" );
document.write( "were the two answers, and so you didn't find the larger.\r\n" );
document.write( "You should have discarded the -7 and kept the 2, then\r\n" );
document.write( "added 5 to the 2 to get +7.\r\n" );
document.write( "\r\n" );
document.write( "When the reciprocal of the larger number is subtracted \r\n" );
document.write( "from the reciprocal of the smaller, the result is 5/14\r\n" );
document.write( "\r\n" );
document.write( "Let x = smaller\r\n" );
document.write( "Larger = x+5  \r\n" );
document.write( "\r\n" );
document.write( "The equation is:\r\n" );
document.write( "\r\n" );
document.write( "\"1%2Fx-1%2F%28x%2B5%29\"\"%22%22=%22%22\"\"5%2F14\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 14x(x+5)\r\n" );
document.write( "\r\n" );
document.write( " 14(x+5) - 14x = 5x(x+5)\r\n" );
document.write( "\r\n" );
document.write( "14x + 70 - 14x = 5x2 + 25x\r\n" );
document.write( "\r\n" );
document.write( "            70 = 5x2 + 25x\r\n" );
document.write( "\r\n" );
document.write( "             0 = 5x2 + 25x - 70\r\n" );
document.write( "\r\n" );
document.write( "Divide through by 5:\r\n" );
document.write( "\r\n" );
document.write( "           \r\n" );
document.write( "             0 = x2 + 5x - 14\r\n" );
document.write( "\r\n" );
document.write( "             0 = (x + 7)(x - 2)\r\n" );
document.write( "\r\n" );
document.write( "                 x + 7 = 0;   x - 2 = 0\r\n" );
document.write( "                     x = -7;      x = 2  <--you mistakenly thought these\r\n" );
document.write( "                                            were the two answers.\r\n" );
document.write( "\r\n" );
document.write( "But we must discard the -7 because it is negative.  Then add 5\r\n" );
document.write( "to the 2 to get the larger.\r\n" );
document.write( "\r\n" );
document.write( "x = smaller = 2\r\n" );
document.write( "Larger = x+5 = 2+5 = 7\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );