document.write( "Question 283152: What is/are the value/s of the inequality $\"%282x%5E2%2B6x-3%29%2F%28x%5E2%2Bx-13%29%3E=1\"$ in interval notation?\r
\n" ); document.write( "\n" ); document.write( "Thank you! \n" ); document.write( "
Algebra.Com's Answer #205615 by Edwin McCravy(20059) $\"\"$ $\"About$
You can put this solution on YOUR website!
$\"%282x%5E2%2B6x-3%29%2F%28x%5E2%2Bx-13%29%3E=1\"$
\n" ); document.write( "
\r\n" );
document.write( "Subtract 1 from both sides to get 0 on the right\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Write  as \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply top and bottom of  by LCD \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Combine the two numerators over the common denominator:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Remove the parentheses:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Combine like terms on top:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Find all critical values by setting numerator and\r\n" );
document.write( "denominator = 0.\r\n" );
document.write( "\r\n" );
document.write( "Setting numerator = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "discriminant = \r\n" );
document.write( "\r\n" );
document.write( "discriminant = \r\n" );
document.write( "\r\n" );
document.write( "discriminant is negative, so we don't\r\n" );
document.write( "get any critical values from the numerator.\r\n" );
document.write( "\r\n" );
document.write( "Setting denominator = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "discriminant = \r\n" );
document.write( "\r\n" );
document.write( "discriminant = \r\n" );
document.write( "\r\n" );
document.write( "So we do get critical values from the\r\n" );
document.write( "denominator:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the two critical values are\r\n" );
document.write( "\r\n" );
document.write( " and \r\n" );
document.write( "\r\n" );
document.write( "These are approximately 3.14 and -4.14\r\n" );
document.write( "\r\n" );
document.write( "Put these on a number line:\r\n" );
document.write( "\r\n" );
document.write( "------o----------------------o-----\r\n" );
document.write( "-6 -5 -4 -3 -2 -1  0  1  2  3  4  5  \r\n" );
document.write( "\r\n" );
document.write( "Choose a whole number value left of -4.14.\r\n" );
document.write( "for a test value.  The easiest is -5\r\n" );
document.write( "\r\n" );
document.write( "Substitute in \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That is a positive number, so we put + signs over \r\n" );
document.write( "that part of the number line:\r\n" );
document.write( "\r\n" );
document.write( " + + +\r\n" );
document.write( "------o----------------------o-----\r\n" );
document.write( "-6 -5 -4 -3 -2 -1  0  1  2  3  4  5\r\n" );
document.write( "\r\n" );
document.write( "Next choose a whole number value between the\r\n" );
document.write( "two critical points for a test value.  The \r\n" );
document.write( "easiest is 0\r\n" );
document.write( "\r\n" );
document.write( "Substitute in \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That is negative so we put - signs over that part \r\n" );
document.write( "of the number line:\r\n" );
document.write( "\r\n" );
document.write( " + + +  - - - - - - - - - - \r\n" );
document.write( "------o----------------------o-----\r\n" );
document.write( "-6 -5 -4 -3 -2 -1  0  1  2  3  4  5\r\n" );
document.write( "\r\n" );
document.write( "Choose a whole number value right of 3.14.\r\n" );
document.write( "for a test value.  The easiest is 4\r\n" );
document.write( "\r\n" );
document.write( "Substitute in \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That is a positive number, so we put + signs over \r\n" );
document.write( "that part of the number line:\r\n" );
document.write( "\r\n" );
document.write( " + + +  - - - - - - - - - -    + + +\r\n" );
document.write( "------o----------------------o------\r\n" );
document.write( "-6 -5 -4 -3 -2 -1  0  1  2  3  4  5\r\n" );
document.write( "\r\n" );
document.write( "Since the inequality of \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "is \r\n" );
document.write( "\r\n" );
document.write( "we choose the intervals with + signs.\r\n" );
document.write( "\r\n" );
document.write( "We cannot include the end points themselves\r\n" );
document.write( "\r\n" );
document.write( "because they cause the denominator to be 0.\r\n" );
document.write( "\r\n" );
document.write( "So the solution set is\r\n" );
document.write( "\r\n" );
document.write( "(,) U (, )\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( " \n" ); document.write( "
\n" );