document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462539>Question 462539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am really having a tough time with this question and would like some insight on how to solve it and what the answer is.\r<BR>\n" );
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document.write( "Find the numbers for which the rational expression is undefined.\r<BR>\n" );
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document.write( "s^3-8s/s^2-81\r<BR>\n" );
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document.write( "Thanks in advance!   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317094 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the numbers for which the rational expression is undefined. <BR>\n" );
document.write( "s^3-8s/s^2-81<BR>\n" );
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document.write( "There are two reasons that rational expressions are undefined in the real number system: (1) the square root of a negative number and (2) division by zero.<BR>\n" );
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document.write( "I want to make sure that I am solving the problem you intend for us to solve. Here is how what you typed would look in a textbook. I explain this one, and another related one further down:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-8s%2Fs%5E2-81 ALIGN=MIDDLE  ALT=\"s%5E3-8s%2Fs%5E2-81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this case, we don't need to worry about the square root of a negative number because there are no square roots! We do need to look more closely at <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8s%2Fs%5E2 ALIGN=MIDDLE  ALT=\"8s%2Fs%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When we divide by s^2, we need to make sure we don't divide by zero. We ask ourselves, what values of s will make s^2=0. We see that when s=0, s^2=0.<BR>\n" );
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document.write( "We would say that <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E3-8s%2Fs%5E2-81 ALIGN=MIDDLE  ALT=\"s%5E3-8s%2Fs%5E2-81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is undefined when s = 0.<BR>\n" );
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document.write( "Here is the problem, I think you may have meant for us to solve:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%5E3-8s%29%2F%28s%5E2-81%29 ALIGN=MIDDLE  ALT=\"%28s%5E3-8s%29%2F%28s%5E2-81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We still don't need to worry about square roots, but we will need to examine<BR>\n" );
document.write( "the denominator of this expression. We do not want the denominator to equal zero, because division by zero is undefined.<BR>\n" );
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document.write( "We ask ourselves which values of s make s^2-81=0. Let's work that out:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2-81=0 ALIGN=MIDDLE  ALT=\"s%5E2-81=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We notice that the left side of the equation is the difference of two squares, so we factor,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%2B9%29%28s-9%29=0 ALIGN=MIDDLE  ALT=\"%28s%2B9%29%28s-9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By the Zero Product Property, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%2B9=0 ALIGN=MIDDLE  ALT=\"s%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-9 ALIGN=MIDDLE  ALT=\"s=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s-9=0 ALIGN=MIDDLE  ALT=\"s-9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=9 ALIGN=MIDDLE  ALT=\"s=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We would say that <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%5E3-8s%29%2F%28s%5E2-81%29 ALIGN=MIDDLE  ALT=\"%28s%5E3-8s%29%2F%28s%5E2-81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is undefined if s = 9 or s = -9.<BR>\n" );
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document.write( "hope this helps!<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex\r<BR>\n" );
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