document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188592>Question 188592</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide. State any restrictions on the variable.\r<BR>\n" );
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document.write( "y^2+5y+4/y^2-49 divide by 2y^2+5y-12/y^2+9y+14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141468 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=141468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%5E2%2B5y%2B4%29%2F%28y%5E2-49%29%29%2F%28%282y%5E2%2B5y-12%29%2F%28y%5E2%2B9y%2B14%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%28y%5E2%2B5y%2B4%29%2F%28y%5E2-49%29%29%28%28y%5E2%2B9y%2B14%29%2F%282y%5E2%2B5y-12%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=%28y%5E2%2B5y%2B4%29%2F%28y%5E2-49%29 ALIGN=MIDDLE  ALT=\"%28y%5E2%2B5y%2B4%29%2F%28y%5E2-49%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=%282y%5E2%2B5y-12%29%2F%28y%5E2%2B9y%2B14%29 ALIGN=MIDDLE  ALT=\"%282y%5E2%2B5y-12%29%2F%28y%5E2%2B9y%2B14%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%28y%2B4%29%28y%2B1%29%29%2F%28y%5E2-49%29%29%28%28y%5E2%2B9y%2B14%29%2F%282y%5E2%2B5y-12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B5y%2B4 ALIGN=MIDDLE  ALT=\"y%5E2%2B5y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B4%29%28y%2B1%29 ALIGN=MIDDLE  ALT=\"%28y%2B4%29%28y%2B1%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%28y%2B4%29%28y%2B1%29%29%2F%28%28y-7%29%28y%2B7%29%29%29%28%28y%5E2%2B9y%2B14%29%2F%282y%5E2%2B5y-12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-49 ALIGN=MIDDLE  ALT=\"y%5E2-49\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-7%29%28y%2B7%29 ALIGN=MIDDLE  ALT=\"%28y-7%29%28y%2B7%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%28y%2B4%29%28y%2B1%29%29%2F%28%28y-7%29%28y%2B7%29%29%29%28%28%28y%2B7%29%28y%2B2%29%29%2F%282y%5E2%2B5y-12%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B9y%2B14 ALIGN=MIDDLE  ALT=\"y%5E2%2B9y%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B7%29%28y%2B2%29 ALIGN=MIDDLE  ALT=\"%28y%2B7%29%28y%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%28%28y%2B4%29%28y%2B1%29%29%2F%28%28y-7%29%28y%2B7%29%29%29%28%28%28y%2B7%29%28y%2B2%29%29%2F%28%28y%2B4%29%282y-3%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=2y%5E2%2B5y-12 ALIGN=MIDDLE  ALT=\"2y%5E2%2B5y-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B4%29%282y-3%29 ALIGN=MIDDLE  ALT=\"%28y%2B4%29%282y-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%28y%2B4%29%28y%2B1%29%28y%2B7%29%28y%2B2%29%29%2F%28%28y-7%29%28y%2B7%29%28y%2B4%29%282y-3%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%28y%2B4%29%29%28y%2B1%29highlight%28%28y%2B7%29%29%28y%2B2%29%29%2F%28%28y-7%29highlight%28%28y%2B7%29%29highlight%28%28y%2B4%29%29%282y-3%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%28y%2B4%29%29%28y%2B1%29cross%28%28y%2B7%29%29%28y%2B2%29%29%2F%28%28y-7%29cross%28%28y%2B7%29%29cross%28%28y%2B4%29%29%282y-3%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=%28%28y%2B1%29%28y%2B2%29%29%2F%28%28y-7%29%282y-3%29%29 ALIGN=MIDDLE  ALT=\"%28%28y%2B1%29%28y%2B2%29%29%2F%28%28y-7%29%282y-3%29%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%28y%5E2%2B5y%2B4%29%2F%28y%5E2-49%29%29%2F%28%282y%5E2%2B5y-12%29%2F%28y%5E2%2B9y%2B14%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=%28%28y%2B1%29%28y%2B2%29%29%2F%28%28y-7%29%282y-3%29%29 ALIGN=MIDDLE  ALT=\"%28%28y%2B1%29%28y%2B2%29%29%2F%28%28y-7%29%282y-3%29%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%28y%5E2%2B5y%2B4%29%2F%28y%5E2-49%29%29%2F%28%282y%5E2%2B5y-12%29%2F%28y%5E2%2B9y%2B14%29%29=%28%28y%2B1%29%28y%2B2%29%29%2F%28%28y-7%29%282y-3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E-7 ALIGN=MIDDLE  ALT=\"y%3C%3E-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E-4 ALIGN=MIDDLE  ALT=\"y%3C%3E-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E-2 ALIGN=MIDDLE  ALT=\"y%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E3%2F2 ALIGN=MIDDLE  ALT=\"y%3C%3E3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C%3E7 ALIGN=MIDDLE  ALT=\"y%3C%3E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these are the restrictions to avoid division by zero).<BR>\n" );
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