document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=989675>Question 989675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2812x%5E2-4%29%2F%28%28x%5E2-1%29%5E3%29+%3C=+0+ ALIGN=MIDDLE  ALT=\"+%2812x%5E2-4%29%2F%28%28x%5E2-1%29%5E3%29+%3C=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >For which of the following values of x does the inequality above hold? \r<BR>\n" );
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document.write( "a. 0\r<BR>\n" );
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document.write( "b. 3/5<BR>\n" );
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document.write( "c. 3/4\r<BR>\n" );
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document.write( "d. &#8722;1/2\r<BR>\n" );
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document.write( "e. &#8722;3/4<BR>\n" );
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document.write( "f. -10\r<BR>\n" );
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document.write( "g. 1\r<BR>\n" );
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document.write( "h. &#8722;9/10<BR>\n" );
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document.write( "Please explain why<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609913 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Pay most attention to the numerator.  THAT needs to be less than or equal zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2-4%3C=0 ALIGN=MIDDLE  ALT=\"12x%5E2-4%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%5E2%3C=4 ALIGN=MIDDLE  ALT=\"12x%5E2%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%3C=1 ALIGN=MIDDLE  ALT=\"3x%5E2%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%3C=1%2F3 ALIGN=MIDDLE  ALT=\"x%5E2%3C=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0%2B-+sqrt%281%2F3%29 ALIGN=MIDDLE  ALT=\"x=0%2B-+sqrt%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----the critical value.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-1 ALIGN=MIDDLE  ALT=\"3x%5E2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a parabola, less than 0 AT and BETWEEN the roots.<BR>\n" );
document.write( "Roots found were <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%281%2F3%29 ALIGN=MIDDLE  ALT=\"-sqrt%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281%2F3%29 ALIGN=MIDDLE  ALT=\"sqrt%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Rationalized, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"-sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "ANSWER:<BR>\n" );
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document.write( "Note that the denominator must not be zero, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E1 ALIGN=MIDDLE  ALT=\"x%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Otherwise,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%283%29%2F3%3C=x%3C=sqrt%283%29%2F3 ALIGN=MIDDLE  ALT=\"-sqrt%283%29%2F3%3C=x%3C=sqrt%283%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > BUT  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E1 ALIGN=MIDDLE  ALT=\"x%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-1 ALIGN=MIDDLE  ALT=\"x%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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