document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135881>Question 135881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: (x-1)/(x+2) > 0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99543 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First let's get your terminology correct.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x%2B2%29+%3E+0 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x%2B2%29+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT an equation, it is an inequality.\r<BR>\n" );
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document.write( "You have already completed step 1 for solving rational inequalities, and that is to arrange the inequality so that you have 0 on one side (generally the right) and everything else on the other side.\r<BR>\n" );
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document.write( "Step 2:  Find the boundary points:\r<BR>\n" );
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document.write( "Step 2A:  Set the numerator equal to zero and solve:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=0 ALIGN=MIDDLE  ALT=\"x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2B:  Set the denominator equal to zero and solve:  <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;\" >  =>  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 3:  Determine whether your solution will be inclusive or exclusive of the boundary points.\r<BR>\n" );
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document.write( "Step 3A:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since the entire fraction must be larger and not equal to zero, the boundary point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be excluded from the solution set because if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > the numerator is equal to zero so the entire fraction would be zero.\r<BR>\n" );
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document.write( "Step 3B:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since a denominator can never be zero, -2 must be excluded from  the solution set.\r<BR>\n" );
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document.write( "Step 4:  Now you have defined three intervals:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >), (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Step 5:  Select any convenient value from the first interval, -3 will do.  Substitute this value into the original inequality:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3-1%29%2F%28-3%2B2%29+=-4%2F-1=4 ALIGN=MIDDLE  ALT=\"%28-3-1%29%2F%28-3%2B2%29+=-4%2F-1=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Since the result is positive, values in this interval are included in the solution set of the inequality.  A positive result means the interval is included because the original inequality has the rational expression greater than zero, or positive.\r<BR>\n" );
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document.write( "Step 6 and 7: Repeat step 5 for the other two intervals:\r<BR>\n" );
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document.write( "Select 0 from the second interval:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280-1%29%2F%280%2B2%29+=-1%2F2 ALIGN=MIDDLE  ALT=\"%280-1%29%2F%280%2B2%29+=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Since the result is negative, values in this interval are excluded.\r<BR>\n" );
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document.write( "Select 2 from the third interval:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-1%29%2F%282%2B2%29+=1%2F4 ALIGN=MIDDLE  ALT=\"%282-1%29%2F%282%2B2%29+=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Again, since the result is positive, values in this interval are included in the solution set of the inequality.\r<BR>\n" );
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document.write( "Therefore your solution set is all real x such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C2 ALIGN=MIDDLE  ALT=\"x%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E1 ALIGN=MIDDLE  ALT=\"x%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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