document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430397>Question 430397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-%288%2Fx%5E2%29%29%2F%28x-%288%2Fx%5E2%29%29 ALIGN=MIDDLE  ALT=\"%282-%288%2Fx%5E2%29%29%2F%28x-%288%2Fx%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For this equation I need to give the domain, asymptotes, and removable discontinuities. I get both of the asymptotes but I just have no idea what the domain and removable discontinuities are. :( Please help me! Thank you and have a great day!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #298948 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=298948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One restriction on the value of x is that it should not be equal to 0.  Another restriction is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-8%2Fx%5E2 ALIGN=MIDDLE  ALT=\"x-8%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be equal to 0.  This is the same as saying that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3+-+8%29%2Fx%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E3+-+8%29%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be equal to 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+8 ALIGN=MIDDLE  ALT=\"x%5E3+-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not equal to 0, or x is not equal to 2.  \r<BR>\n" );
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document.write( "The DOMAIN is then all real numbers not equal to 0 or 2. This said, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-%288%2Fx%5E2%29%29%2F%28x-%288%2Fx%5E2%29%29+=+%28%282x%5E2-8%29%2F%28x%5E2%29%29%2F%28%28x%5E3+-+8%29%2Fx%5E2%29=%28%282%28x%5E2+-+4%29%29%2Fx%5E2%29%2F%28%28x-2%29%28x%5E2+%2B+2x%2B4%29%2Fx%5E2%29=+%282x%5E2%28x-2%29%28x%2B2%29%29%2F%28x%5E2%28x-2%29%28x%5E2+%2B+2x+%2B+4%29%29%0D%0A%0D%0A=+%282%28x%2B2%29%29%2F%28x%5E2+%2B+2x+%2B+4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "As x goes to infinity, the expression goes to y = 0, because the degree of the numerator is less than the degree of the denominator.  (Because the expression will have no real roots.)  \r<BR>\n" );
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document.write( "Hence y = 0 is a HORIZONTAL ASYMPTOTE.  \r<BR>\n" );
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document.write( "Since the denominator is a quadratic irreducible over the real numbers, the expression has NO VERTICAL ASYMPTOTES.\r<BR>\n" );
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document.write( "There are REMOVABLE DISCONTINUITIES at x = 0 and x = 2, because they cancel out in the process of simplification.  They correspond to \"holes\" at the graph at the point (0,1) and (2, 2/3). <BR>\n" );
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