document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86530>Question 86530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> divide\r<BR>\n" );
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document.write( "2x-6<BR>\n" );
document.write( "over<BR>\n" );
document.write( "21<BR>\n" );
document.write( "divided by<BR>\n" );
document.write( "5x-15<BR>\n" );
document.write( "over <BR>\n" );
document.write( "12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62747 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=62747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+6%29%2F21 ALIGN=MIDDLE  ALT=\"%282x+-+6%29%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide it by:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x+-+15%29%2F12 ALIGN=MIDDLE  ALT=\"%285x+-+15%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Recall the \"arithmetic\" rule about fractions.  If you are dividing by a fraction you can<BR>\n" );
document.write( "invert the divisor and multiply it by the dividend.  In this case it means you can  take<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+-+6%29%2F21 ALIGN=MIDDLE  ALT=\"%282x+-+6%29%2F21\"   DISABLED_style= \"max-width:90%; height:auto;\" > and multiply it by the inversion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x+-+15%29%2F12 ALIGN=MIDDLE  ALT=\"%285x+-+15%29%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get the answer<BR>\n" );
document.write( "to this problem. After the inversion, the original division problem is converted to the<BR>\n" );
document.write( "following multiplication problem:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282x+-+6%29%2F21%29%2A%2812%2F%285x-15%29%29 ALIGN=MIDDLE  ALT=\"%28%282x+-+6%29%2F21%29%2A%2812%2F%285x-15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Before it gets too complicated, let's do some factoring. Note that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+6 ALIGN=MIDDLE  ALT=\"2x+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28x+-+3%29 ALIGN=MIDDLE  ALT=\"2%2A%28x+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+21 ALIGN=MIDDLE  ALT=\"+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A3 ALIGN=MIDDLE  ALT=\"7%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A3 ALIGN=MIDDLE  ALT=\"4%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x+-+15 ALIGN=MIDDLE  ALT=\"5x+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A%28x-3%29 ALIGN=MIDDLE  ALT=\"5%2A%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute all these factored forms into the appropriate places in the multiplication<BR>\n" );
document.write( "problem and it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2A%28x-3%29%29%2F%287%2A3%29%29%2A%28%284%2A3%29%2F%285%2A%28x-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28%282%2A%28x-3%29%29%2F%287%2A3%29%29%2A%28%284%2A3%29%2F%285%2A%28x-3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel all the terms that appear in the numerator with a corresponding appearance in<BR>\n" );
document.write( "the denominator as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28cross%28x-3%29%29%2F%287%2A%28cross%283%29%29%29%2A4%2A%28cross%283%29%29%2F%285%2A%28cross%28x-3%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The remaining factors in the numerator are 4 and 2. They multiply out to 8. And the remaining<BR>\n" );
document.write( "factors in the denominator are 7 and 5 and they multiply out to 35.  This makes the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F35 ALIGN=MIDDLE  ALT=\"8%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > and there are no more common factors in the numerator and the denominator.<BR>\n" );
document.write( "So this cannot be reduced further and the answer to the original problem is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F35 ALIGN=MIDDLE  ALT=\"8%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope this helps you to understand the division process in this problem.<BR>\n" );
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