document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146834>Question 146834</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how would i do this? Simplify the following fractions by putting them in lowest terms or by performing the indicated operations\r<BR>\n" );
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document.write( "81-x to the 4th over 3-x divided by 9+x2 over 9 = </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108298 by </B><A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><B>mangopeeler07(462)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mangopeeler07><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=108298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2881-x%5E4%29%2F%283-x%29 ALIGN=MIDDLE  ALT=\"%2881-x%5E4%29%2F%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2Bx%5E2%29%2F%289%29 ALIGN=MIDDLE  ALT=\"%289%2Bx%5E2%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Find the common denominator, which would be 9(3-x).  Manipulate the fractions and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2881-x%5E4%29%29%2F9%283-x%29 ALIGN=MIDDLE  ALT=\"%289%2881-x%5E4%29%29%2F9%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283-x%29%289%2Bx%5E2%29%29%2F%289%283-x%29%29 ALIGN=MIDDLE  ALT=\"%28%283-x%29%289%2Bx%5E2%29%29%2F%289%283-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Then eliminate the denominators from the equation.  Get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2881-x%5E4%29 ALIGN=MIDDLE  ALT=\"9%2881-x%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > divided by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-x%29%289%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"%283-x%29%289%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "Factor all of the expressions.  The expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81-x%5E4 ALIGN=MIDDLE  ALT=\"81-x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2Bx%5E2%29%289-x%5E2%29 ALIGN=MIDDLE  ALT=\"%289%2Bx%5E2%29%289-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-x%5E2 ALIGN=MIDDLE  ALT=\"9-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-x%29%283%2Bx%29 ALIGN=MIDDLE  ALT=\"%283-x%29%283%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So the numerator becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%289%2Bx%5E2%29%283-x%29%283%2Bx%29 ALIGN=MIDDLE  ALT=\"9%289%2Bx%5E2%29%283-x%29%283%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > while the denominator remains <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2Bx%5E2%29%283-x%29 ALIGN=MIDDLE  ALT=\"%289%2Bx%5E2%29%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it looks like: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%289%2Bx%5E2%29%283-x%29%283%2Bx%29%29%2F%28%289%2Bx%5E2%29%283-x%29%29 ALIGN=MIDDLE  ALT=\"%289%289%2Bx%5E2%29%283-x%29%283%2Bx%29%29%2F%28%289%2Bx%5E2%29%283-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Now just cancel out like terms in the numerator and the denominator, which would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283-x%29 ALIGN=MIDDLE  ALT=\"%283-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"%289%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then you are left with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%283%2Bx%29%29%2F1 ALIGN=MIDDLE  ALT=\"%289%283%2Bx%29%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%283%2Bx%29 ALIGN=MIDDLE  ALT=\"9%283%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You can stop there if you want to. Going further is not necessary, but if you want to anyway, read on.\r<BR>\n" );
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document.write( "It is very easy from here.  Just distribute the 9 to both terms and get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2827%2B9x%29%2F1 ALIGN=MIDDLE  ALT=\"%2827%2B9x%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or simply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2B9x ALIGN=MIDDLE  ALT=\"27%2B9x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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