document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=169942>Question 169942</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Divide and, if possible, simplify\r<BR>\n" );
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document.write( "z^2 + 8z + 16/z^2 + 13z + 36 divided by z^2 + 4z/z^2 + 15z + 54 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125438 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=125438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28z%5E2%2B8z%2B16%29%2F%28z%5E2%2B13z%2B36%29%29%2F%28%28z%5E2%2B4z%29%2F%28z%5E2%2B15z%2B54%29%29 ALIGN=MIDDLE   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%28z%5E2%2B8z%2B16%29%2F%28z%5E2%2B13z%2B36%29%29%28%28z%5E2%2B15z%2B54%29%2F%28z%5E2%2B4z%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=%28z%5E2%2B8z%2B16%29%2F%28z%5E2%2B13z%2B36%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%2B8z%2B16%29%2F%28z%5E2%2B13z%2B36%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=%28z%5E2%2B4z%29%2F%28z%5E2%2B15z%2B54%29 ALIGN=MIDDLE  ALT=\"%28z%5E2%2B4z%29%2F%28z%5E2%2B15z%2B54%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%28z%2B4%29%28z%2B4%29%29%2F%28z%5E2%2B13z%2B36%29%29%28%28z%5E2%2B15z%2B54%29%2F%28z%5E2%2B4z%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2%2B8z%2B16 ALIGN=MIDDLE  ALT=\"z%5E2%2B8z%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B4%29%28z%2B4%29 ALIGN=MIDDLE  ALT=\"%28z%2B4%29%28z%2B4%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%28z%2B4%29%28z%2B4%29%29%2F%28%28z%2B9%29%28z%2B4%29%29%29%28%28z%5E2%2B15z%2B54%29%2F%28z%5E2%2B4z%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2%2B13z%2B36 ALIGN=MIDDLE  ALT=\"z%5E2%2B13z%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B9%29%28z%2B4%29 ALIGN=MIDDLE  ALT=\"%28z%2B9%29%28z%2B4%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%28z%2B4%29%28z%2B4%29%29%2F%28%28z%2B9%29%28z%2B4%29%29%29%28%28%28z%2B9%29%28z%2B6%29%29%2F%28z%5E2%2B4z%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2%2B15z%2B54 ALIGN=MIDDLE  ALT=\"z%5E2%2B15z%2B54\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B9%29%28z%2B6%29 ALIGN=MIDDLE  ALT=\"%28z%2B9%29%28z%2B6%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%28z%2B4%29%28z%2B4%29%29%2F%28%28z%2B9%29%28z%2B4%29%29%29%28%28%28z%2B9%29%28z%2B6%29%29%2F%28z%28z%2B4%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=z%5E2%2B4z ALIGN=MIDDLE  ALT=\"z%5E2%2B4z\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%28z%2B4%29 ALIGN=MIDDLE  ALT=\"z%28z%2B4%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%28z%2B4%29%28z%2B4%29%28z%2B9%29%28z%2B6%29%29%2F%28z%28z%2B9%29%28z%2B4%29%28z%2B4%29%29 ALIGN=MIDDLE   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=%28highlight%28%28z%2B4%29%29highlight%28%28z%2B4%29%29highlight%28%28z%2B9%29%29%28z%2B6%29%29%2F%28z%2Ahighlight%28%28z%2B9%29%29highlight%28%28z%2B4%29%29highlight%28%28z%2B4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Highlight the common terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28cross%28%28z%2B4%29%29cross%28%28z%2B4%29%29cross%28%28z%2B9%29%29%28z%2B6%29%29%2F%28z%2Across%28%28z%2B9%29%29cross%28%28z%2B4%29%29cross%28%28z%2B4%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Cancel out the common terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B6%29%2F%28z%29 ALIGN=MIDDLE  ALT=\"%28z%2B6%29%2F%28z%29\"   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%28z%5E2%2B8z%2B16%29%2F%28z%5E2%2B13z%2B36%29%29%2F%28%28z%5E2%2B4z%29%2F%28z%5E2%2B15z%2B54%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=%28z%2B6%29%2F%28z%29 ALIGN=MIDDLE  ALT=\"%28z%2B6%29%2F%28z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28z%5E2%2B8z%2B16%29%2F%28z%5E2%2B13z%2B36%29%29%2F%28%28z%5E2%2B4z%29%2F%28z%5E2%2B15z%2B54%29%29=%28z%2B6%29%2F%28z%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%3C%3E-9 ALIGN=MIDDLE  ALT=\"z%3C%3E-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%3C%3E-6 ALIGN=MIDDLE  ALT=\"z%3C%3E-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%3C%3E-4 ALIGN=MIDDLE  ALT=\"z%3C%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%3C%3E0 ALIGN=MIDDLE  ALT=\"z%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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