document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121085>Question 121085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation (4w-1)/(3w+6)-(w-1)/3=(w-1)/w+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88823 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=88823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284w-1%29%2F%283w%2B6%29-%28w-1%29%2F%283%29=%28w-1%29%2F%28w%2B2%29 ALIGN=MIDDLE  ALT=\"%284w-1%29%2F%283w%2B6%29-%28w-1%29%2F%283%29=%28w-1%29%2F%28w%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283w%2B6%29%283%29%28w%2B2%29%29%28%284w-1%29%2F%28cross%283w%2B6%29%29-%28w-1%29%2F%28cross%283%29%29%29=%28%283w%2B6%29%283%29%28w%2B2%29%29%28%28w-1%29%2F%28cross%28w%2B2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283w%2B6%29%283%29%28w%2B2%29 ALIGN=MIDDLE  ALT=\"%283w%2B6%29%283%29%28w%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Doing this will eliminate every fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%28w%2B2%29%284w-1%29-%283w%2B6%29%28w%2B2%29%28w-1%29=%283w%2B6%29%283%29%28w-1%29 ALIGN=MIDDLE  ALT=\"%283%29%28w%2B2%29%284w-1%29-%283w%2B6%29%28w%2B2%29%28w-1%29=%283w%2B6%29%283%29%28w-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply. Notice every denominator has been canceled out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%284w%5E2%2B7w-2%29-%283w%2B6%29%28w%5E2%2Bw-2%29=3%283w%5E2%2B3w-6%29 ALIGN=MIDDLE  ALT=\"%283%29%284w%5E2%2B7w-2%29-%283w%2B6%29%28w%5E2%2Bw-2%29=3%283w%5E2%2B3w-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%284w%5E2%2B7w-2%29-%283w%5E3%2B9w%5E2-12%29=3%283w%5E2%2B3w-6%29 ALIGN=MIDDLE  ALT=\"%283%29%284w%5E2%2B7w-2%29-%283w%5E3%2B9w%5E2-12%29=3%283w%5E2%2B3w-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w%2B6 ALIGN=MIDDLE  ALT=\"3w%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2Bw-2 ALIGN=MIDDLE  ALT=\"w%5E2%2Bw-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w%5E3%2B9w%5E2-12 ALIGN=MIDDLE  ALT=\"3w%5E3%2B9w%5E2-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12w%5E2%2B21w-6-3w%5E3-9w%5E2%2B12=9w%5E2%2B9w-18 ALIGN=MIDDLE  ALT=\"12w%5E2%2B21w-6-3w%5E3-9w%5E2%2B12=9w%5E2%2B9w-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3w%5E3-6w%5E2%2B12w%2B24=0 ALIGN=MIDDLE  ALT=\"-3w%5E3-6w%5E2%2B12w%2B24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get everything to the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%28w%5E2-4%29%28w%2B2%29=0 ALIGN=MIDDLE  ALT=\"-3%28w%5E2-4%29%28w%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side\r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2-4=0 ALIGN=MIDDLE  ALT=\"w%5E2-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2B2=0 ALIGN=MIDDLE  ALT=\"w%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now solve for w for each factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=2 ALIGN=MIDDLE  ALT=\"w=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-2 ALIGN=MIDDLE  ALT=\"w=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=2 ALIGN=MIDDLE  ALT=\"w=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-2 ALIGN=MIDDLE  ALT=\"w=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, if we plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-2 ALIGN=MIDDLE  ALT=\"w=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the original equation, we'll get a zero denominator. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-2 ALIGN=MIDDLE  ALT=\"w=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <b>not</b> a possible solution\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So our solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=2 ALIGN=MIDDLE  ALT=\"w=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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