document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208584>Question 208584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all numbers for which the rational expression is undefined\r<BR>\n" );
document.write( "\n" );
document.write( "q^3 - 5q/ q^2-9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158460 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=158460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equation is:<BR>\n" );
document.write( "(q^3 - 5q) / (q^2-9)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "q^2 - 9 is the product of:<BR>\n" );
document.write( "(q-3)<BR>\n" );
document.write( "and <BR>\n" );
document.write( "(q+3)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since q^2 - 9 is in the denominator, this means that the denominator will be 0 when q = 3 and when q = -3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "when the denominator is 0, the equation is undefined, because the result of a division by 0 is undefined.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a graph of your equation would look like this:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-4%2C4%2C-30%2C30%2C%28x%5E3-5x%29+%2F+%28x%5E2-9%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-4%2C4%2C-30%2C30%2C%28x%5E3-5x%29+%2F+%28x%5E2-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "a longer range view would be:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-20%2C20%2C-40%2C40%2C%28x%5E3-5x%29+%2F+%28x%5E2-9%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-20%2C20%2C-40%2C40%2C%28x%5E3-5x%29+%2F+%28x%5E2-9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the y values when x = -3 and when x = 3 are undefined because you can't divide a real number by 0 and get a real number as an answer.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "as x gets closer to 3 or -3, the value of y approaches infinity or minus infinity.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the vertical lines you see are called asymptotes.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the graph doesn't really show it all too well, but the y value goes way up or down as you approach x = 3 and x = -3.  off the charts so to speak.  if the resolution was a lot better, you would be able to see it a lot better.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );