document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767173>Question 767173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain of the function.\r<BR>\n" );
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document.write( "h(x) = ln[(x^2)/(x-4)]\r<BR>\n" );
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document.write( "What I have tried on the problem so far is as follows:\r<BR>\n" );
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document.write( "[(x^2)/(x-4)] > 0\r<BR>\n" );
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document.write( "(x-4) * [(x^2)/(x-4)] > 0 * (x-4)\r<BR>\n" );
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document.write( "x^3 - 4x^2 > 0\r<BR>\n" );
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document.write( "x^2 (x-4) > 0<BR>\n" );
document.write( "-(x-4)          -(x-4)\r<BR>\n" );
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document.write( "x^2 > -x-4<BR>\n" );
document.write( "+x       +x\r<BR>\n" );
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document.write( "x^2 +x > -4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467464 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You started out ok.  The argument of the log function must be strictly greater than zero.\r<BR>\n" );
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document.write( "But consider just your numerator:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2\ >\ 0\ \forall\ x\ \not =\ 0\">.  So far, we have to exclude 0.\r<BR>\n" );
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document.write( "But the denominator is positive so long as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ >\ 4\">, a restriction that includes <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ \not =\ 0\">\r<BR>\n" );
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document.write( "Hence the domain is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{x\ \in\ \mathbb{R}\ :\ x\ >\ 4\right\}\">\r<BR>\n" );
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document.write( "Note the strictly greater than relationship because the value 4 itself must be excluded to avoid division by zero.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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