document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29867>Question 29867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the domain of the function h(x) = 3x/ x(x^2-81).\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16643 by </B><A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><B>sdmmadam@yahoo.com(530)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sdmmadam@yahoo.com><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=16643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h(x) = 3x/ x(x^2-81).<BR>\n" );
document.write( "That is h(x) = 3/(x^2-81) (canceling x not zero)<BR>\n" );
document.write( "Since division by zero is not defined, h(x) cannot be defined for (x^2-81)=0<BR>\n" );
document.write( "And (x^2-81) = 0 <BR>\n" );
document.write( "implies (x+9)(x-9) = 0 (using a^2-b^2 = (a+b)(a-b) where a = x and b = 9)<BR>\n" );
document.write( "that is for (x+9)=0 giving x=-9 and for (x-9) = 0 giving x = 9<BR>\n" );
document.write( "Therefore the funciton h(x) is defined for all x EXCEPTING x = 9 and x = -9<BR>\n" );
document.write( "Therefore the domain of the given function is the complement of {-9,9} in the real number system R<BR>\n" );
document.write( "That is Domain = R - {-9,9} </SPAN>\n" );
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