document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117935>Question 117935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide the following fractions.\r<BR>\n" );
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document.write( "6p-18               3p-9<BR>\n" );
document.write( "-----  divided by  ------<BR>\n" );
document.write( " 9p                p^2+2p </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85941 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=85941\">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=%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29 ALIGN=MIDDLE  ALT=\"%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%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=%28%286p-18%29%2F%289p%29%29%2A%28%28%28p%5E2%2B2p%29%29%2F%28%283p-9%29%29%29 ALIGN=MIDDLE  ALT=\"%28%286p-18%29%2F%289p%29%29%2A%28%28%28p%5E2%2B2p%29%29%2F%28%283p-9%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction by the reciprocal of the second fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286%28p-3%29%29%2F%289p%29%29%28%28p%5E2%2B2p%29%2F%283p-9%29%29 ALIGN=MIDDLE  ALT=\"%28%286%28p-3%29%29%2F%289p%29%29%28%28p%5E2%2B2p%29%2F%283p-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6p-18 ALIGN=MIDDLE  ALT=\"6p-18\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28p-3%29 ALIGN=MIDDLE  ALT=\"6%28p-3%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=%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%5E2%2B2p%29%2F%283p-9%29%29 ALIGN=MIDDLE  ALT=\"%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%5E2%2B2p%29%2F%283p-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9p ALIGN=MIDDLE  ALT=\"9p\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%28p%29 ALIGN=MIDDLE  ALT=\"9%28p%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=%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283p-9%29%29 ALIGN=MIDDLE  ALT=\"%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283p-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2%2B2p ALIGN=MIDDLE  ALT=\"p%5E2%2B2p\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28p%2B2%29 ALIGN=MIDDLE  ALT=\"p%28p%2B2%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=%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283%28p-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28%286%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283%28p-3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3p-9 ALIGN=MIDDLE  ALT=\"3p-9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28p-3%29 ALIGN=MIDDLE  ALT=\"3%28p-3%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=%28%28%282%2A3%29%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283%28p-3%29%29%29 ALIGN=MIDDLE  ALT=\"%28%28%282%2A3%29%28p-3%29%29%2F%289%28p%29%29%29%28%28p%28p%2B2%29%29%2F%283%28p-3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Factor 6 into 2*3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2A3%29%28p-3%29p%28p%2B2%29%2F9%28p%293%28p-3%29 ALIGN=MIDDLE  ALT=\"%282%2A3%29%28p-3%29p%28p%2B2%29%2F9%28p%293%28p-3%29\"   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=%282%2Across%283%29%29cross%28%28p-3%29%29cross%28p%29%28p%2B2%29%2F9cross%28p%29cross%283%29cross%28%28p-3%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=2%28p%2B2%29%2F9 ALIGN=MIDDLE  ALT=\"2%28p%2B2%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29 ALIGN=MIDDLE  ALT=\"%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28p%2B2%29%2F9 ALIGN=MIDDLE  ALT=\"2%28p%2B2%29%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Note: This is not a typo even though this answer is identical to the previous one. The previous expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286p-18%29%2F%283p-9%29%29%2F%28%289p%29%2F%28p%5E2%2B2p%29%29 ALIGN=MIDDLE  ALT=\"%28%286p-18%29%2F%283p-9%29%29%2F%28%289p%29%2F%28p%5E2%2B2p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29 ALIGN=MIDDLE  ALT=\"%28%286p-18%29%2F%289p%29%29%2F%28%283p-9%29%2F%28p%5E2%2B2p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Can you see why?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286p-18%29%2F%283p-9%29%29%2F%28%289p%29%2F%28p%5E2%2B2p%29%29 ALIGN=MIDDLE  ALT=\"%28%286p-18%29%2F%283p-9%29%29%2F%28%289p%29%2F%28p%5E2%2B2p%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286p-18%29%2F%283p-9%29%29%2A%28%28%28p%5E2%2B2p%29%29%2F%28%289p%29%29%29 ALIGN=MIDDLE  ALT=\"%28%286p-18%29%2F%283p-9%29%29%2A%28%28%28p%5E2%2B2p%29%29%2F%28%289p%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and \r<BR>\n" );
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document.write( "For each second expression, notice the denominators have swapped. Since they all get combined in one big denominator, the answer does not change. </SPAN>\n" );
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