document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166665>Question 166665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me express the following rational expressiond in lowest terms.\r<BR>\n" );
document.write( "\n" );
document.write( "1) 4z/8z-12\r<BR>\n" );
document.write( "\n" );
document.write( "2) y^5-3y^3+8y^2/5y\r<BR>\n" );
document.write( "\n" );
document.write( "3) z^3+4z^2/z^2-8z+16\r<BR>\n" );
document.write( "\n" );
document.write( "i am totally lost.any help would be great. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122831 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=122831\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "# 1\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=%284z%29%2F%288z-12%29 ALIGN=MIDDLE  ALT=\"%284z%29%2F%288z-12%29\"   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=%284z%29%2F%284%282z-3%29%29 ALIGN=MIDDLE  ALT=\"%284z%29%2F%284%282z-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8z-12 ALIGN=MIDDLE  ALT=\"8z-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%282z-3%29 ALIGN=MIDDLE  ALT=\"4%282z-3%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=%28highlight%284%29z%29%2F%28highlight%284%29%282z-3%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%284%29z%29%2F%28highlight%284%29%282z-3%29%29\"   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%284%29z%29%2F%28cross%284%29%282z-3%29%29 ALIGN=MIDDLE  ALT=\"%28cross%284%29z%29%2F%28cross%284%29%282z-3%29%29\"   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=%28z%29%2F%282z-3%29 ALIGN=MIDDLE  ALT=\"%28z%29%2F%282z-3%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( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284z%29%2F%288z-12%29 ALIGN=MIDDLE  ALT=\"%284z%29%2F%288z-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%29%2F%282z-3%29 ALIGN=MIDDLE  ALT=\"%28z%29%2F%282z-3%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=%284z%29%2F%288z-12%29=%28z%29%2F%282z-3%29 ALIGN=MIDDLE  ALT=\"%284z%29%2F%288z-12%29=%28z%29%2F%282z-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%3C%3E3%2F2 ALIGN=MIDDLE  ALT=\"z%3C%3E3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "# 2\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=%28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29 ALIGN=MIDDLE  ALT=\"%28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29\"   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=%28y%5E2%28y%5E3-3y%2B8%29%29%2F%285y%29 ALIGN=MIDDLE  ALT=\"%28y%5E2%28y%5E3-3y%2B8%29%29%2F%285y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E5-3y%5E3%2B8y%5E2 ALIGN=MIDDLE  ALT=\"y%5E5-3y%5E3%2B8y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2A%28y%5E3-3%2Ay%2B8%29 ALIGN=MIDDLE  ALT=\"y%5E2%2A%28y%5E3-3%2Ay%2B8%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=%28y%2Ay%28y%5E3-3y%2B8%29%29%2F%285y%29 ALIGN=MIDDLE  ALT=\"%28y%2Ay%28y%5E3-3y%2B8%29%29%2F%285y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Ay ALIGN=MIDDLE  ALT=\"y%2Ay\"   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=%28y%2Ahighlight%28y%29%28y%5E3-3y%2B8%29%29%2F%285%2Ahighlight%28y%29%29 ALIGN=MIDDLE  ALT=\"%28y%2Ahighlight%28y%29%28y%5E3-3y%2B8%29%29%2F%285%2Ahighlight%28y%29%29\"   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=%28y%2Across%28y%29%28y%5E3-3y%2B8%29%29%2F%285%2Across%28y%29%29 ALIGN=MIDDLE  ALT=\"%28y%2Across%28y%29%28y%5E3-3y%2B8%29%29%2F%285%2Across%28y%29%29\"   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=%28y%28y%5E3-3y%2B8%29%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%28y%28y%5E3-3y%2B8%29%29%2F%285%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=%28y%5E4-3y%5E2%2B8y%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%28y%5E4-3y%5E2%2B8y%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<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=%28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29 ALIGN=MIDDLE  ALT=\"%28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E4-3y%5E2%2B8y%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%28y%5E4-3y%5E2%2B8y%29%2F%285%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=%28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29=%28y%5E4-3y%5E2%2B8y%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%28y%5E5-3y%5E3%2B8y%5E2%29%2F%285y%29=%28y%5E4-3y%5E2%2B8y%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E0 ALIGN=MIDDLE  ALT=\"y%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "# 3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Are you sure that the numerator is not <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3-4z%5E2 ALIGN=MIDDLE  ALT=\"z%5E3-4z%5E2\"   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=%28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29 ALIGN=MIDDLE  ALT=\"%28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29\"   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=%28z%5E2%2A%28z-4%29%29%2F%28z%5E2-8z%2B16%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%2A%28z-4%29%29%2F%28z%5E2-8z%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2 ALIGN=MIDDLE  ALT=\"z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3-4z%5E2 ALIGN=MIDDLE  ALT=\"z%5E3-4z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2%2A%28z-4%29 ALIGN=MIDDLE  ALT=\"z%5E2%2A%28z-4%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=%28z%5E2%2A%28z-4%29%29%2F%28%28z-4%29%28z-4%29%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%2A%28z-4%29%29%2F%28%28z-4%29%28z-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2-8z%2B16 ALIGN=MIDDLE  ALT=\"z%5E2-8z%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-4%29%5E2 ALIGN=MIDDLE  ALT=\"%28z-4%29%5E2\"   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=%28z%5E2%2Ahighlight%28z-4%29%29%2F%28highlight%28z-4%29%28z-4%29%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%2Ahighlight%28z-4%29%29%2F%28highlight%28z-4%29%28z-4%29%29\"   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=%28z%5E2%2Across%28z-4%29%29%2F%28cross%28z-4%29%28z-4%29%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%2Across%28z-4%29%29%2F%28cross%28z-4%29%28z-4%29%29\"   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=%28z%5E2%29%2F%28z-4%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%29%2F%28z-4%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( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29 ALIGN=MIDDLE  ALT=\"%28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%5E2%29%2F%28z-4%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%29%2F%28z-4%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=%28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29=%28z%5E2%29%2F%28z-4%29 ALIGN=MIDDLE  ALT=\"%28z%5E3-4z%5E2%29%2F%28z%5E2-8z%2B16%29=%28z%5E2%29%2F%28z-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%3C%3E4 ALIGN=MIDDLE  ALT=\"z%3C%3E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );