document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912127>Question 912127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to solve the x- and y- and asymptotes of these rational functions?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2%2B1%29%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"y=%28x%5E2%2B1%29%2F%28x-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=y=%281%2F6%29%28x-1%29%5E3%28x%2B2%29%5E2%286-x%29 ALIGN=MIDDLE  ALT=\"y=%281%2F6%29%28x-1%29%5E3%28x%2B2%29%5E2%286-x%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=y=%282x%2B1%29%2F%285-3x%29 ALIGN=MIDDLE  ALT=\"y=%282x%2B1%29%2F%285-3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "please explain,<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553633 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=553633\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your second equation with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > factor is a polynomial and has no asymptotes.  \r<BR>\n" );
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document.write( "Your third equation has horizontal asymptote of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > toward the left and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > toward the right; which you can tell by seeing degree of numerator and denominator are the same and examining each extreme case.  A vertical asymptote is for 5-3x=0 meaning <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F3 ALIGN=MIDDLE  ALT=\"x=5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the vertical asymptote.\r<BR>\n" );
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document.write( "First equation is undefined for x=3 so this is the vertical asymptote.  Degree of numerator is one more than degree of denominator, so ... you can find the slant asymptote; perform the division and consider what happens to the remainder for x extreme in either direction.  The quotient tells you the slant asymptote. </SPAN>\n" );
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