document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32056>Question 32056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1/(x+2))+(2/(x-3))<=1\r<BR>\n" );
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document.write( "here is my work:<BR>\n" );
document.write( "((x-3)+2(x+2)-((x+2)(x-3)))/((x+2)(x-3))<=0<BR>\n" );
document.write( "you then simplify to get:<BR>\n" );
document.write( "(-x^2 +2x +7)/((x+2)(x-3))<=0<BR>\n" );
document.write( "but when you use the quadratic equation it is very ugly.\r<BR>\n" );
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document.write( "Thank you,<BR>\n" );
document.write( "Alexus </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18599 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=18599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's see:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28x%2B2%29%29%2B%282%2F%28x-3%29%29%3C=1 ALIGN=MIDDLE  ALT=\"%281%2F%28x%2B2%29%29%2B%282%2F%28x-3%29%29%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the fractions on the left.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-3%29%2B2%28x%2B2%29%29%2F%28%28x%2B2%29%28x-3%29%29+%3C=1 ALIGN=MIDDLE  ALT=\"%28%28x-3%29%2B2%28x%2B2%29%29%2F%28%28x%2B2%29%28x-3%29%29+%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29%28x-3%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3%2B2x%2B4+%3C=+%28x%2B2%29%28x-3%29 ALIGN=MIDDLE  ALT=\"x-3%2B2x%2B4+%3C=+%28x%2B2%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B1%3C=x%5E2-x-6 ALIGN=MIDDLE  ALT=\"3x%2B1%3C=x%5E2-x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B1%29 ALIGN=MIDDLE  ALT=\"%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C=x%5E2-4x-7 ALIGN=MIDDLE  ALT=\"0%3C=x%5E2-4x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x-7%3E=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x-7%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Begin by solving the quadratic equation<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x-7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-4x-7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Solve for x using the quadratic formula<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2B-sqrt%2816%2B28%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%284%2B-sqrt%2816%2B28%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2B-sqrt%2844%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%284%2B-sqrt%2844%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%284%2B-2sqrt%2811%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%284%2B-2sqrt%2811%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2B-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"x=2%2B-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-intercepts are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+=+2%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2-sqrt%2811%29 ALIGN=MIDDLE  ALT=\"x+=+2-sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But since we are solving:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4x-7%3E=0 ALIGN=MIDDLE  ALT=\"x%5E2-4x-7%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > we are looking for x-values with positve y-values. Looking at the graph of the quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-3%2C6%2C-12%2C5%2Cx%5E2-4x-7%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-3%2C6%2C-12%2C5%2Cx%5E2-4x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The solution set is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=2-sqrt%2811%29orx%3E=2%2Bsqrt%2811%29 ALIGN=MIDDLE  ALT=\"x%3C=2-sqrt%2811%29orx%3E=2%2Bsqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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