document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196861>Question 196861</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me simplify this rational expression: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29%29%2F%28%283x%5E3-3x%5E2y%2B3xy%5E2%29%2F%286x%5E2-6y%5E2%29%29 ALIGN=MIDDLE   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 #147591 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=147591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: the previous solution has a sign error and the answer should be much simpler.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29%29%2F%28%283x%5E3-3x%5E2y%2B3xy%5E2%29%2F%286x%5E2-6y%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29%29%28%286x%5E2-6y%5E2%29%2F%283x%5E3-3x%5E2y%2B3xy%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the first fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29 ALIGN=MIDDLE  ALT=\"%28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by the reciprocal of the second fraction <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%5E3-3x%5E2y%2B3xy%5E2%29%2F%286x%5E2-6y%5E2%29 ALIGN=MIDDLE  ALT=\"%283x%5E3-3x%5E2y%2B3xy%5E2%29%2F%286x%5E2-6y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2By%29%28x%5E2-xy%2By%5E2%29%29%2F%282x%5E3%2B2x%5E2y%29%29%28%286x%5E2-6y%5E2%29%2F%283x%5E3-3x%5E2y%2B3xy%5E2%29%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%2By%5E3 ALIGN=MIDDLE  ALT=\"x%5E3%2By%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x%5E2-xy%2By%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x%5E2-xy%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2By%29%28x%5E2-xy%2By%5E2%29%29%2F%282x%5E2%28x%2By%29%29%29%28%286x%5E2-6y%5E2%29%2F%283x%5E3-3x%5E2y%2B3xy%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E3%2B2x%5E2y ALIGN=MIDDLE  ALT=\"2x%5E3%2B2x%5E2y\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%28x%2By%29 ALIGN=MIDDLE  ALT=\"2x%5E2%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2By%29%28x%5E2-xy%2By%5E2%29%29%2F%282x%5E2%28x%2By%29%29%29%28%286%28x-y%29%28x%2By%29%29%2F%283x%5E3-3x%5E2y%2B3xy%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-6y%5E2 ALIGN=MIDDLE  ALT=\"6x%5E2-6y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28x-y%29%28x%2By%29 ALIGN=MIDDLE  ALT=\"6%28x-y%29%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28x%2By%29%28x%5E2-xy%2By%5E2%29%29%2F%282x%5E2%28x%2By%29%29%29%28%286%28x-y%29%28x%2By%29%29%2F%283x%28x%5E2-xy%2By%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E3-3x%5E2y%2B3xy%5E2 ALIGN=MIDDLE  ALT=\"3x%5E3-3x%5E2y%2B3xy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%28x%5E2-xy%2By%5E2%29 ALIGN=MIDDLE  ALT=\"3x%28x%5E2-xy%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%28x%2By%29%28x%5E2-xy%2By%5E2%29%28x-y%29%28x%2By%29%29%2F%282x%5E2%2A3x%28x%2By%29%28x%5E2-xy%2By%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the fractions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%28x%2By%29%28x%5E2-xy%2By%5E2%29%28x-y%29%28x%2By%29%29%2F%286x%5E3%28x%2By%29%28x%5E2-xy%2By%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E3 ALIGN=MIDDLE  ALT=\"6x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%286%29%2Ahighlight%28%28x%2By%29%29highlight%28%28x%5E2-xy%2By%5E2%29%29%28x-y%29%28x%2By%29%29%2F%28highlight%286%29x%5E3%2Ahighlight%28%28x%2By%29%29highlight%28%28x%5E2-xy%2By%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%286%29%2Across%28%28x%2By%29%29cross%28%28x%5E2-xy%2By%5E2%29%29%28x-y%29%28x%2By%29%29%2F%28cross%286%29x%5E3%2Across%28%28x%2By%29%29cross%28%28x%5E2-xy%2By%5E2%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-y%29%28x%2By%29%29%2F%28x%5E3%29 ALIGN=MIDDLE  ALT=\"%28%28x-y%29%28x%2By%29%29%2F%28x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-y%5E2%29%2F%28x%5E3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-y%5E2%29%2F%28x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29%29%2F%28%283x%5E3-3x%5E2y%2B3xy%5E2%29%2F%286x%5E2-6y%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-y%5E2%29%2F%28x%5E3%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-y%5E2%29%2F%28x%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%5E3%2By%5E3%29%2F%282x%5E3%2B2x%5E2y%29%29%2F%28%283x%5E3-3x%5E2y%2B3xy%5E2%29%2F%286x%5E2-6y%5E2%29%29=%28x%5E2-y%5E2%29%2F%28x%5E3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );