document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622641>Question 622641</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help! Divide.\r<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 #391497 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=391497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given to divide:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%283y%2B12%29%2F%288y%5E3%29%29%2F%28%289y%2B36%29%2F%2816y%5E3%29%29+ ALIGN=MIDDLE  ALT=\"+%28%283y%2B12%29%2F%288y%5E3%29%29%2F%28%289y%2B36%29%2F%2816y%5E3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that this is one great big fraction. The numerator is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%283y%2B12%29%2F%288y%5E3%29%29 ALIGN=MIDDLE  ALT=\"+%28%283y%2B12%29%2F%288y%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the denominator is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%289y%2B36%29%2F%2816y%5E3%29%29+ ALIGN=MIDDLE  ALT=\"%28%289y%2B36%29%2F%2816y%5E3%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So you are dividing the numerator by the denominator. Remember the rule for dividing by a fraction ... namely that you can divide by a fraction by inverting the fractional divisor and then multiplying that inverted fraction by the number you are dividing into.<BR>\n" );
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document.write( "When you invert the denominator you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2816y%5E3%29%2F%289y+%2B+36%29%29+ ALIGN=MIDDLE  ALT=\"%28%2816y%5E3%29%2F%289y+%2B+36%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now multiply that inverted fraction times the numerator and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283y%2B12%29%2F%288y%5E3%29%29%2A%28%2816y%5E3%29%2F%289y+%2B+36%29%29+ ALIGN=MIDDLE  ALT=\"%28%283y%2B12%29%2F%288y%5E3%29%29%2A%28%2816y%5E3%29%2F%289y+%2B+36%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that the denominator of the first fraction is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y%5E3 ALIGN=MIDDLE  ALT=\"8y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it will divide into the numerator of the second fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16y%5E3 ALIGN=MIDDLE  ALT=\"16y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to give just 2.  This reduces the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283y%2B12%29%2F1%29%2A%28%282%29%2F%289y+%2B+36%29%29+ ALIGN=MIDDLE  ALT=\"%28%283y%2B12%29%2F1%29%2A%28%282%29%2F%289y+%2B+36%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next note that the denominator of the second fraction can be factored by 9 to give:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283y%2B12%29%2F1%29%2A%282%2F%289%28y+%2B+4%29%29%29+ ALIGN=MIDDLE  ALT=\"%28%283y%2B12%29%2F1%29%2A%282%2F%289%28y+%2B+4%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then the numerator of the first fraction can be factored by 3 to result in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%28y%2B4%29%29%2F%281%29%29%2A%28%282%29%2F%289%28y+%2B+4%29%29%29+ ALIGN=MIDDLE  ALT=\"%28%283%28y%2B4%29%29%2F%281%29%29%2A%28%282%29%2F%289%28y+%2B+4%29%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So you have a (y+4) factor in the numerator and a (y+4) factor in the denominator. These cancel out and you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F1%29%2A%282%2F9%29 ALIGN=MIDDLE  ALT=\"%283%2F1%29%2A%282%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which after multiplication gives:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A2%29%2F9+=+6%2F9 ALIGN=MIDDLE  ALT=\"%283%2A2%29%2F9+=+6%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and 6 divided by 9 is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "and that is the answer to this problem.<BR>\n" );
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document.write( "I hope this helps you to see your way through this problem <BR>\n" );
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