document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773404>Question 773404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the domain and what are the zero(s) of the this function : (9x^(3)-4x)/((x-3)(x^(2)-2x+1))\r<BR>\n" );
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document.write( "I have tried long division, simplifying it, and rearranging the equation. I can't find any zero(s) or the domain. Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471532 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=471532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289x%5E%283%29-4x%29%2F%28%28x-3%29%28x%5E%282%29-2x%2B1%29%29 ALIGN=MIDDLE  ALT=\"%289x%5E%283%29-4x%29%2F%28%28x-3%29%28x%5E%282%29-2x%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The domain is the set of acceptable values for x.  The denominator of the function must not be zero, so looking at the two factors of the denominator, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E3 ALIGN=MIDDLE  ALT=\"x%3C%3E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E1 ALIGN=MIDDLE  ALT=\"x%3C%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <BR>\n" );
document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x%2B1=%28x-1%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-2x%2B1=%28x-1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Use the numerator to look for zeros of the function.  This is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%289x%5E2-4%29 ALIGN=MIDDLE  ALT=\"x%289x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this becomes zero when x=0 and when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%284%2F9%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%284%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%284%2F9%29 ALIGN=MIDDLE  ALT=\"x=sqrt%284%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; or stated more simply, the zeros of the function are x from the set { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B2%2F3 ALIGN=MIDDLE  ALT=\"%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > }. </SPAN>\n" );
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