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 #88822 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=88822\">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=%284w-1%29%2F%283w%2B6%29-%28w-1%29%2F3=%28w-1%29%2F%28w%2B2%29 ALIGN=MIDDLE  ALT=\"%284w-1%29%2F%283w%2B6%29-%28w-1%29%2F3=%28w-1%29%2F%28w%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1 is to put your variable on one side, so add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28%28w-1%29%2F%28w%2B2%29%29 ALIGN=MIDDLE  ALT=\"-%28%28w-1%29%2F%28w%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides of the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284w-1%29%2F%283w%2B6%29-%28w-1%29%2F3-%28w-1%29%2F%28w%2B2%29=0 ALIGN=MIDDLE  ALT=\"%284w-1%29%2F%283w%2B6%29-%28w-1%29%2F3-%28w-1%29%2F%28w%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we need a common denominator.  Notice that <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;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%28w%2B2%29 ALIGN=MIDDLE  ALT=\"3%2A%28w%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and those two factors are the other two denominators.  Therefore, <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;\" > is our lowest common denominator.\r<BR>\n" );
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document.write( "We can leave the first term alone, but the second term has to be multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B2%29%2F%28w%2B2%29 ALIGN=MIDDLE  ALT=\"%28w%2B2%29%2F%28w%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the third term must be multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   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=%284w-1%29%2F%283w%2B6%29-%28%28w-1%29%28w%2B2%29%29%2F%283w%2B6%29-3%28w-1%29%2F%283w%2B6%29=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now is a good time to note that since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2B2 ALIGN=MIDDLE  ALT=\"w%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor in the denominator, we need to exclude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the solution set because that would make a denominator or denominators in the original equation go to zero.\r<BR>\n" );
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document.write( "Multiply the binomial factors and distribute the 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284w-1-w%5E2-w%2B2-3w%2B3%29%2F%283w%2B6%29=0 ALIGN=MIDDLE  ALT=\"%284w-1-w%5E2-w%2B2-3w%2B3%29%2F%283w%2B6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Collect terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4-w%5E2=0 ALIGN=MIDDLE  ALT=\"4-w%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor the difference of two squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-w%29%282%2Bw%29=0 ALIGN=MIDDLE  ALT=\"%282-w%29%282%2Bw%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-w=0 ALIGN=MIDDLE  ALT=\"2-w=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Bw=0 ALIGN=MIDDLE  ALT=\"2%2Bw=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in other words, <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;\" >.  But remember, we have to exclude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the solution set because that value makes the original equation undefined.  In the process of applying the common denominator, we introduced the square of the variable and that process introduced an extraneous root.\r<BR>\n" );
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document.write( "<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;\" > is the only root of the equation. </SPAN>\n" );
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