document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927749>Question 927749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> give the equations of any vertical and horizontal asymptotes of the rational functions f(x)= (8x+9)/(x^2-4)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563216 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=563216\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%288x%2B9%29%2F%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%288x%2B9%29%2F%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=domain ALIGN=MIDDLE  ALT=\"domain\"   DISABLED_style= \"max-width:90%; height:auto;\" > , because whichever values are not allowed in the domain will be vertical asymptotes on the graph\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>vertical asymptotes \r<BR>\n" );
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document.write( "domain:<BR>\n" );
document.write( "{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-2 ALIGN=MIDDLE  ALT=\"x%3C%3E-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E2 ALIGN=MIDDLE  ALT=\"x%3C%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontal ALIGN=MIDDLE  ALT=\"horizontal\"   DISABLED_style= \"max-width:90%; height:auto;\" > asymptote is found by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dividing ALIGN=MIDDLE  ALT=\"dividing\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=leading ALIGN=MIDDLE  ALT=\"leading\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=terms ALIGN=MIDDLE  ALT=\"terms\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the asymptote is given by:\r<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+ ALIGN=MIDDLE  ALT=\"y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= (numerator's leading coefficient)/(denominator's leading coefficient)\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=%280%2Ax%5E2%2B8x%2B9%29%2F%28x%5E2-4%29=0%2F1=0 ALIGN=MIDDLE  ALT=\"y+=%280%2Ax%5E2%2B8x%2B9%29%2F%28x%5E2-4%29=0%2F1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontal ALIGN=MIDDLE  ALT=\"horizontal\"   DISABLED_style= \"max-width:90%; height:auto;\" > asymptote is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=0 ALIGN=MIDDLE  ALT=\"y+=0\"   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=drawing%28600%2C600%2C-10%2C10%2C-10%2C10%2Crectangle%28-2%2C-11%2C11%2C11%29%2Crectangle%282%2C-11%2C11%2C11%29%2Cgraph%28+600%2C+600%2C+-10%2C10%2C+-10%2C+10%2C+%288x%2B9%29%2F%28x%5E2-4%29%2C0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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