document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103968>Question 103968</A>: <I><SPAN STYLE=\"word-break: break-all;\">     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE  ALT=\"%283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75643 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=75643\">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=%283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE  ALT=\"%283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B27 ALIGN=MIDDLE  ALT=\"x%5E3%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x%5E2-3x%2B9%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x%5E2-3x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this means the LCM is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x%5E2-3x%2B9%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x%5E2-3x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since every denominator has either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B9 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or both). So we want every fraction to have a denominator of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28x%5E2-3x%2B9%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28x%5E2-3x%2B9%29\"   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=%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28%28x%5E2-3x%2B9%29%2F%28x%5E2-3x%2B9%29%29%28x%2F%28x%2B3%29%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the second fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-3x%2B9%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-3x%2B9%29%2F%28x%5E2-3x%2B9%29\"   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=%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+x%28x%5E2-3x%2B9%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE   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=%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%28%28x%2B3%29%2F%28x%2B3%29%29%28%282x%5E2%29%2F%28x%5E2-3x%2B9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the third fraction by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%2F%28x%2B3%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%2F%28x%2B3%29\"   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=%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%282x%5E2%29%28x%2B3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+-+%28x%5E3-3x%5E2%2B9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29%2B+%0D%0A%282x%5E3%2B6x%5E2%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "Since we have a common denominator, we can combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3-+%28x%5E3-3x%5E2%2B9x%29%2B2x%5E3%2B6x%5E2%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3-x%5E3%2B3x%5E2-9x%2B2x%5E3%2B6x%5E2%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ ALIGN=MIDDLE  ALT=\"%283x%5E3-x%5E3%2B3x%5E2-9x%2B2x%5E3%2B6x%5E2%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E3%2B9x%5E2-9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ ALIGN=MIDDLE  ALT=\"%284x%5E3%2B9x%5E2-9x%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%284x%5E2-3x%29%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+ ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%284x%5E2-3x%29%29%2F%28%28x%2B3%29%28x%5E2-3x%2B9%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the numerator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%28x%2B3%29%29%284x%5E2-3x%29%29%2F%28cross%28%28x%2B3%29%29%28x%5E2-3x%2B9%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-3x%29%2F%28x%5E2-3x%2B9%29+ ALIGN=MIDDLE  ALT=\"%284x%5E2-3x%29%2F%28x%5E2-3x%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%284x-3%29%29%2F%28x%5E2-3x%2B9%29+ ALIGN=MIDDLE  ALT=\"%28x%284x-3%29%29%2F%28x%5E2-3x%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out an x\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29 ALIGN=MIDDLE  ALT=\"%283x%5E3%29%2F%28x%5E3%2B27%29+-+x%2F%28x%2B3%29+%2B+%282x%5E2%29%2F%28x%5E2-3x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%284x-3%29%29%2F%28x%5E2-3x%2B9%29+ ALIGN=MIDDLE  ALT=\"%28x%284x-3%29%29%2F%28x%5E2-3x%2B9%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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