document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001468>Question 1001468</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x%5E2+-+a%5E2%29%2F%28x+-+a%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x%5E2+-+a%5E2%29%2F%28x+-+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , when I find the value when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, its <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2F0 ALIGN=MIDDLE  ALT=\"0%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is, well you know.\r<BR>\n" );
document.write( "\n" );
document.write( "But when I further simplify the function, I get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x+%2B+a ALIGN=MIDDLE  ALT=\"f%28x%29+=+x+%2B+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which has a value for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+a ALIGN=MIDDLE  ALT=\"x+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a ALIGN=MIDDLE  ALT=\"2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Is it a problem in maths or what? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618636 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> no - there's no problem at all.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the simplified equation is a new and separate equation from the original equation it was derived from.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the domain of the simplified equation is different from the domain of the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "there are rules for analyzing rational functions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the simplified equation is useful to tell you whrere the asymptotes are.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "but you can't expect the simplified equation to have the same undefined points as the original equation because it's a different equation that stands on its own.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "an example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "find the vertical asymptotes for y = ((x-1)*(x+1))/((x-1)*(x+5))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y is undefined at x = 1 and x = -5, but there is a vertical asymptote only at x = -5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's the graph:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C%28%28x-1%29%2A%28x%2B1%29%29%2F%28%28x-1%29%2A%28x%2B5%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can see from the graph that there is a vertical asymptote at x = -5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what you can't see is that the value of the function is undefined at x = 1, but there is a hole there, even if there is no asymptote.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "what has happened is that the (x-1) cancels out and you get the simplified equation that only has (x+5) in the denominator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the factor in the denominator cancels out when you simplify the eqaution, there is no vertical asymptote at that point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if it doesn't cancel out, there is an asymptote at that point.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the following table will, however, show you that the value of the original equation is undefined at x = 1 and at x = -5, while the value of the simplified equation is only undefined at x = -5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/110501.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the original equation and the simplified equation are two different equations with two different domains.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the simplified equation is useful to tell you what the value of the hole is in the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's some references that might help you to understand better.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut40_ratgraph.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut40_ratgraph.htm</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://sites.csn.edu/istewart/mathweb/math126/graph_rational_func/graph_rational_func.htm\" target = \"_blank\">http://sites.csn.edu/istewart/mathweb/math126/graph_rational_func/graph_rational_func.htm</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );