document.write( "Question 44639This question is from textbook College Algebra
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Solve the inequality and graph the \r\n" );
document.write( "solution on a real number line \r\n" );
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document.write( "1/x > 1/(x+3)
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Algebra.Com's Answer #29535 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Solve the inequality and graph the \r\n" );
document.write( "solution on a real number line \r\n" );
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document.write( "1/x > 1/(x+3)\r\n" );
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document.write( "1/x - 1/(x+3) > 0\r\n" );
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document.write( "(x+3) - x\r\n" );
document.write( "--------- > 0\r\n" );
document.write( "  x(x+3)\r\n" );
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document.write( "    3\r\n" );
document.write( "-------- > 0\r\n" );
document.write( " x(x+3)\r\n" );
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document.write( "The critical values are x=0 and x=-3\r\n" );
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document.write( "Mark those on a number line:\r\n" );
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document.write( "<----------o--------o----------->\r\n" );
document.write( "          -3        0\r\n" );
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document.write( "Choose a value left of (less than) -3, say -4\r\n" );
document.write( "and substitute it into \r\n" );
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document.write( "    3\r\n" );
document.write( "-------- \r\n" );
document.write( " x(x+3)\r\n" );
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document.write( "    3          3\r\n" );
document.write( "---------- = ---- which is positive \r\n" );
document.write( " -4(-4+3)      4\r\n" );
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document.write( "so our number line becomes\r\n" );
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document.write( " ++++++++++\r\n" );
document.write( "<----------o--------o----------->\r\n" );
document.write( "          -3        0\r\n" );
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document.write( "Choose a value between -3 and 0, say -1\r\n" );
document.write( "and substitute it in \r\n" );
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document.write( "    3\r\n" );
document.write( "-------- \r\n" );
document.write( " x(x+3)\r\n" );
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document.write( "    3          3\r\n" );
document.write( "---------- = ---- which is negative \r\n" );
document.write( " -1(-1+3)     -2\r\n" );
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document.write( "so our number line becomes\r\n" );
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document.write( " ++++++++++ --------\r\n" );
document.write( "<----------o--------o----------->\r\n" );
document.write( "          -3        0\r\n" );
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document.write( "Choose a value right of 0, that is , \r\n" );
document.write( "greater than 0, say 1, and substitute\r\n" );
document.write( "it into \r\n" );
document.write( "\r\n" );
document.write( "    3\r\n" );
document.write( "-------- \r\n" );
document.write( " x(x+3)\r\n" );
document.write( "\r\n" );
document.write( "    3          3\r\n" );
document.write( "---------- = ---- which is positive \r\n" );
document.write( " 1(1+3)        4\r\n" );
document.write( "\r\n" );
document.write( "so our number line becomes\r\n" );
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document.write( " ++++++++++ -------- +++++++++++\r\n" );
document.write( "<----------o--------o----------->\r\n" );
document.write( "          -3        0\r\n" );
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document.write( "The expression\r\n" );
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document.write( "    3\r\n" );
document.write( "-------- \r\n" );
document.write( " x(x+3)\r\n" );
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document.write( "is not defined at the endpoints\r\n" );
document.write( "0 or -3, so the solution, since\r\n" );
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document.write( "    3\r\n" );
document.write( "-------- > 0\r\n" );
document.write( " x(x+3)\r\n" );
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document.write( "requires the left side to be non-negative,\r\n" );
document.write( "the solution set in interval notation is\r\n" );
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document.write( "(-oo, -3) U (0, oo)\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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