document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636364>Question 636364</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function g is defined below.\r<BR>\n" );
document.write( "\n" );
document.write( "      <BR>\n" );
document.write( "      g(x)=(x-9)/(x^2-12x+3)<BR>\n" );
document.write( "      <BR>\n" );
document.write( "     <BR>\n" );
document.write( "Find all values of x that are NOT in the domain of g.\r<BR>\n" );
document.write( "\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #400956 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=400956\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "      <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x-9%29%2F%28x%5E2-12x%2B3%29 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x-9%29%2F%28x%5E2-12x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the domain of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29 ALIGN=MIDDLE  ALT=\"g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=all ALIGN=MIDDLE  ALT=\"all\"   DISABLED_style= \"max-width:90%; height:auto;\" > real numbers (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=except ALIGN=MIDDLE  ALT=\"except\"   DISABLED_style= \"max-width:90%; height:auto;\" > the roots of denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-12x%2B3 ALIGN=MIDDLE  ALT=\"x%5E2-12x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >; as you already know, denominator could NOT be equal to zero. \r<BR>\n" );
document.write( "\n" );
document.write( "To find out what they are, solve using quadratic formula:\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
document.write( "\n" );
document.write( "  <BR>\n" );
document.write( "  Starting with the general quadratic<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  the general solution using the quadratic equation is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-12%2Ax%2B3=0 ALIGN=MIDDLE  ALT=\"x%5E2-12%2Ax%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-12 ALIGN=MIDDLE  ALT=\"b=-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=3 ALIGN=MIDDLE  ALT=\"c=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--12+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28--12+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-12, and c=3<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -12 to get 12<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+sqrt%28+144-4%2A1%2A3+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+144-4%2A1%2A3+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -12 to get 144  (note: remember when you square -12, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%5E2=-12%2A-12=144 ALIGN=MIDDLE  ALT=\"%28-12%29%5E2=-12%2A-12=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+sqrt%28+144%2B-12+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+144%2B-12+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A3%2A1 ALIGN=MIDDLE  ALT=\"-4%2A3%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12 ALIGN=MIDDLE  ALT=\"-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+sqrt%28+132+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+132+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+2%2Asqrt%2833%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+2%2Asqrt%2833%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B-+2%2Asqrt%2833%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+2%2Asqrt%2833%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So now the expression breaks down into two parts<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+%2B+2%2Asqrt%2833%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B+2%2Asqrt%2833%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2812+-+2%2Asqrt%2833%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2812+-+2%2Asqrt%2833%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now break up the fraction<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B12%2F2%2B2%2Asqrt%2833%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2B12%2F2%2B2%2Asqrt%2833%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B12%2F2-2%2Asqrt%2833%29%2F2 ALIGN=MIDDLE  ALT=\"x=%2B12%2F2-2%2Asqrt%2833%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Simplify<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2Bsqrt%2833%29 ALIGN=MIDDLE  ALT=\"x=6%2Bsqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-sqrt%2833%29 ALIGN=MIDDLE  ALT=\"x=6-sqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  So the solutions are:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2Bsqrt%2833%29 ALIGN=MIDDLE  ALT=\"x=6%2Bsqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-sqrt%2833%29 ALIGN=MIDDLE  ALT=\"x=6-sqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, all values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the domain of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the solutions \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6%2Bsqrt%2833%29 ALIGN=MIDDLE  ALT=\"x=6%2Bsqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=and ALIGN=MIDDLE  ALT=\"and\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6-sqrt%2833%29 ALIGN=MIDDLE  ALT=\"x=6-sqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );