document.write( "Question 1092731: May I have some help with this question please? I have to solve the equation and inequality and show all steps and work. It's one homework problem from the summer and I am still not clear on it. The \"0\" is confusing to me. \r
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Algebra.Com's Answer #707332 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "There are 2 (two) critical points: x= 3, where the numerator becomes equal to zero, and x= -2, where the denominator becomes equal to zero.\r\n" );
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document.write( "And there are 3 (three) intervals on the number line:\r\n" );
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document.write( "   1)   < x < -2,\r\n" );
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document.write( "   2)  -2 < x < 3,   and\r\n" );
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document.write( "   3)  3 < x < .\r\n" );
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document.write( "On the interval 1)  both the numerator and denominator are negative;  so, the left side rational function is positive.\r\n" );
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document.write( "On the interval 2)  the denominator is positive, while the numerator is negative.  So, the left side rational function is negative.\r\n" );
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document.write( "On the interval 3)  both the numerator and denominator are positive.  So, the left side rational function is positive.\r\n" );
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document.write( "Conclusion.  The solution to the given inequality is the UNION of two intervals  (-infinity,-2) U (3,infinity).\r\n" );
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document.write( "See the plot below as an illustration.\r\n" );
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document.write( "Plot y = \r\n" );
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\n" ); document.write( "\n" ); document.write( "This is the standard way and the sample/template on how the solution of similar problems should be made and presented   (as mantra . . . )\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Solving inequalities for rational functions with numerator and denominator factored into a product of linear binomials \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Inequalities\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I\r
\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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