document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=435914>Question 435914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> asymptotes <BR>\n" );
document.write( "f(x)=(3x^2-7x-6)/(2x^2-18) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301637 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=301637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The asymptotes will occur when the denominator is 0 and the numerator is nonzero.\r<BR>\n" );
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document.write( "The denominator is 0 when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+18+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-+18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3 ALIGN=MIDDLE  ALT=\"x+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. However, when x = 3 we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+0%2F0 ALIGN=MIDDLE  ALT=\"f%283%29+=+0%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is indeterminate, and no asymptote occurs (there is a hole in the graph instead). Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-3%29+%3C%3E+0 ALIGN=MIDDLE  ALT=\"f%28-3%29+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is the only asymptote.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%283x%5E2-7x-6%29%2F%282x%5E2-18%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%283x%5E2-7x-6%29%2F%282x%5E2-18%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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