document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=741841>Question 741841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find asymptotes and holes for (x+4)(x-2) all over (x-6)(x-2)<BR>\n" );
document.write( "and graph<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-2%29%2F%28%28x-6%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-2%29%2F%28%28x-6%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #452179 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</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=452179\">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=%28x%2B4%29%28x-2%29%2F%28%28x-6%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-2%29%2F%28%28x-6%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Vertical asymptote at x=6, because that would be where the function is undefined due to x-6 being in the denominator as a factor.  Division by zero is impossible.\r<BR>\n" );
document.write( "\n" );
document.write( "A hole is at x=2, because the binomial factor, x-2 is a factor in both the numerator and the denominator, giving the expression (x-2)/(x-2), which is 1; yet this expression IS still part of the rational expression given, and with x-2 in the denominator, x cannot be +2, since this would create a division by 0 when x=2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Please note here, the hole at x=2 is not appearing properly:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B4%29%28x-2%29%2F%28%28x-6%29%28x-2%29%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B4%29%28x-2%29%2F%28%28x-6%29%28x-2%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );