document.write( "Question 26445: The sum of the reciprocals of two consecutive even numbers is 7/24. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #14293 by AnlytcPhil(1806) $\"\"$ $\"About$

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The sum of the reciprocals of two consecutive even numbers is 7/24.\r\n" );
document.write( "Find the numbers.\r\n" );
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document.write( "Let smaller even integer = x\r\n" );
document.write( "Then larger even integer = x + 2\r\n" );
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document.write( "\"Reciprocal of\" means \"1 over\"\r\n" );
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document.write( " 1      1       7\r\n" );
document.write( "--- + ----- = ---- \r\n" );
document.write( " x     x+2     24\r\n" );
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document.write( "The LCD is 24x(x+2).  Multiply through by that LCD\r\n" );
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document.write( "          1               1                7\r\n" );
document.write( "24x(x+2)·--- + 24x(x+2)·----- = 24x(x+2)·---- \r\n" );
document.write( "          x              x+2              24\r\n" );
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document.write( "Cancel what will cancel\r\n" );
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document.write( "          1               1                7\r\n" );
document.write( "24x(x+2)·--- + 24x(x+2)·----- = 24x(x+2)·---- \r\n" );
document.write( "          x              x+2              24\r\n" );
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document.write( "                 24(x+2) + 24x = x(x+2)·7 \r\n" );
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document.write( "                24x + 48 + 24x = (x²+2x)7\r\n" );
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document.write( "                      48x + 48 = 7x² + 14x\r\n" );
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document.write( "                             0 = 7x² - 34x - 48 \r\n" );
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document.write( "                             0 = (7x + 8)(x - 6)\r\n" );
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document.write( "                Set first factor = 0\r\n" );
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document.write( "                                  7x + 8 = 0\r\n" );
document.write( "                                      7x = -8\r\n" );
document.write( "                                       x = -8/7\r\n" );
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document.write( "                Set second factor = 0\r\n" );
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document.write( "                                    x - 6 = 0\r\n" );
document.write( "                                        x = 6\r\n" );
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document.write( "Discard fraction answer.  Solution: smaller = 6, larger = 6+2 or 8\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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