document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132558>Question 132558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all numbers for which the rational expression is undefined.\r<BR>\n" );
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document.write( "I can't remember how to do this.\r<BR>\n" );
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document.write( "m^3 - 4m <BR>\n" );
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document.write( "m^2 - 64\r<BR>\n" );
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document.write( "This is supposed to look like a fraction.  I can't figure out how to set it up.  Sorry. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #96871 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=96871\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find all numbers for which the rational expression is undefined:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5E3-4m%29%2F%28m%5E2-64%29 ALIGN=MIDDLE  ALT=\"%28m%5E3-4m%29%2F%28m%5E2-64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ok, such an expression will be undefined whenever the denominator equals zero.<BR>\n" );
document.write( "So, if you set the denominator (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-64 ALIGN=MIDDLE  ALT=\"m%5E2-64\"   DISABLED_style= \"max-width:90%; height:auto;\" >) equal to zero then solve for the varable m, you will have your answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2-64+=+0 ALIGN=MIDDLE  ALT=\"m%5E2-64+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 64 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2+=+64 ALIGN=MIDDLE  ALT=\"m%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+8 ALIGN=MIDDLE  ALT=\"m+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+-8 ALIGN=MIDDLE  ALT=\"m+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > These are the numbers that make the expression undefined.<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28m%5E3-4m%29%2F%28m%5E2-64%29 ALIGN=MIDDLE  ALT=\"%28m%5E3-4m%29%2F%28m%5E2-64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute m = 8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%5E3-4%288%29%29%2F%288%5E2-64%29 ALIGN=MIDDLE  ALT=\"%288%5E3-4%288%29%29%2F%288%5E2-64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28512-32%29%2F%2864-64%29 ALIGN=MIDDLE  ALT=\"%28512-32%29%2F%2864-64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=480%2F0 ALIGN=MIDDLE  ALT=\"480%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Division by zero is undefined!<BR>\n" );
document.write( "Similarly for m = -8<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-8%29%5E3-4%28-8%29%29%2F%28%28-8%29%5E2+-+64%29 ALIGN=MIDDLE  ALT=\"%28%28-8%29%5E3-4%28-8%29%29%2F%28%28-8%29%5E2+-+64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-512%2B32%29%2F%2864-64%29 ALIGN=MIDDLE  ALT=\"%28-512%2B32%29%2F%2864-64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-480%29%2F0 ALIGN=MIDDLE  ALT=\"%28-480%29%2F0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Division by zero is undefined! </SPAN>\n" );
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