document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=12352>Question 12352</A>: <I><SPAN STYLE=\"word-break: break-all;\">  how am I to solve an inequality of this type(x+2)(x+2)/(x+1)<0 using cases </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #6318 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=6318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x%2B2%29%2F%28x%2B1%29%3C0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x%2B2%29%2F%28x%2B1%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B2%29%5E2%2F%28x%2B1%29+%3C+0+ ALIGN=MIDDLE  ALT=\"+%28x%2B2%29%5E2%2F%28x%2B1%29+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " Hence,the numberator and the denominator are of different sign.<BR>\n" );
document.write( " But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B2%29%5E2+%3E=+0+ ALIGN=MIDDLE  ALT=\"+%28x%2B2%29%5E2+%3E=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real x.<BR>\n" );
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document.write( " The denomiator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B1+ ALIGN=MIDDLE  ALT=\"+x%2B1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be negative and the nmerator<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2+ ALIGN=MIDDLE  ALT=\"x%2B2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be 0.<BR>\n" );
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document.write( " So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B2%29%5E2%2F%28x%2B1%29+%3C+0+ ALIGN=MIDDLE  ALT=\"+%28x%2B2%29%5E2%2F%28x%2B1%29+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > implies<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B1%3C0+and+x+is+not+equal+to+-2 ALIGN=MIDDLE  ALT=\"+x%2B1%3C0+and+x+is+not+equal+to+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( " We obtain the solution set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-2+%3C+x+%3C+-1+or+x+%3C+-2 ALIGN=MIDDLE  ALT=\"+-2+%3C+x+%3C+-1+or+x+%3C+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " In the interval notaion: (-oo,-2) U (-2,-1).\r<BR>\n" );
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document.write( " The above is the shortest way to solve this kind of questions.<BR>\n" );
document.write( " Try to think about it. [In fact, I can get the answer by direct view<BR>\n" );
document.write( " in a second. ]\r<BR>\n" );
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document.write( " If you really want to consider cases\r<BR>\n" );
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document.write( " Look the sign of the given  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%5E2%2F%28x%2B1%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2F%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the intervals<BR>\n" );
document.write( " (-oo,-2),(-2,-1), (-1,+oo). You will see.<BR>\n" );
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document.write( "           <BR>\n" );
document.write( " -----------*-----*----------------------<BR>\n" );
document.write( " -oo        -2    -1                  +oo\r<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
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